Discussion:
Why I Prefer IRV to Condorcet
Greg
2008-11-19 21:28:29 UTC
Permalink
I have written up my reasons for preferring IRV over Condorcet methods
in an essay, the current draft of which is available here:
http://www.gregdennis.com/voting/irv_vs_condorcet.html

I welcome any comments you have.

Thanks,
Greg
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Kevin Venzke
2008-11-20 01:09:28 UTC
Permalink
Hi Greg,
Objet: [EM] Why I Prefer IRV to Condorcet
Date: Mercredi 19 Novembre 2008, 15h28
I have written up my reasons for preferring IRV over
Condorcet methods
http://www.gregdennis.com/voting/irv_vs_condorcet.html
I welcome any comments you have.
Thanks,
Greg
I want to comment on the first point/reason. I'll quote from the page.
First and foremost, IRV eliminates the most common type of Condorcet
failure --- the "spoiler" scenario --- where the presence of a candidate
with little core support causes a Condorcet winner with strong core
support to lose.
I don't understand what kind of scenario you're referring to. I thought I
did, and was going to say that good Condorcet methods don't behave in
that way. But then I noticed the term "core support," which puzzles me
in the context of Condorcet spoilers.
Admittedly, there is another situation similar to the spoiler problem ---
the "center squeeze" scenario -- in which IRV may fail to elect the
Condorcet winner. In this scenario, the presence of a candidate with
strong core support causes a Condorcet winner with little core support to
lose. Fortunately, despite the theoretical possibility of this scenario,
the empirical evidence suggests that it is vanishingly rare in practice.
Despite the hundreds of public IRV elections that are conducted worldwide
every year, the actual concrete examples of it occurring in practice are
few and far between.
A problem with using IRV elections to judge whether IRV suffers from
a center squeeze effect, is that it overlooks the possibility that IRV's
nomination incentives deter would-be Condorcet winners from running
(due to the fact that everyone knows they would not win).

You can make the argument that plurality also has very good Condorcet
efficiency since it is never observed to fail to elect a Condorcet winner.
Even adding the ability to rank lower preferences would probably not
change this, since with no real change to the method there is also no
real change to the nomination incentives.
Lacking sufficient examples of real elections in which IRV has failed to
elect the Condorcet winner, a few IRV critics have resorted to using top-
two runoff elections in which the Condorcet winner lost as evidence of
IRV's center-squeeze problem. However, top-two runoff and instant runoff
are different systems that can produce different results, so
this "evidence" is hardly convincing.
Actually some of us will argue that top-two runoff seems likely to have
better Condorcet efficiency (in the abstract sense) than IRV. I can see
an argument for both sides. But I would agree that they are different
systems with different incentives.


I have a few problems with #4... Partly that I find the arguments
speculative wrt candidate behavior, and partly that I don't see an
inherent advantage in knowing where candidates stand if everything is
still going to come down to competing blocs of core support that probably
dislike each other. Mostly, and related, it's that if we agree that we
can't trust voters to give us meaningful lower preferences, then I lose
most of my enthuasism for voting methods. If we can only trust first
preferences, and candidates that get a lot of first preferences, how much
room do we really have to make improvements? We can stray from plurality
hardly at all.

Kevin Venzke




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Chris Benham
2008-11-20 19:51:01 UTC
Permalink
Greg,
I generally liked your essay. I rate IRV as the best of the single-winner methods that
meet Later-no-Harm, and a good method (and a vast improvement on FPP).

But I think you made a couple of technical errors.

"However, because bullet voting can help and never backfire against one's top choice under
Condorcet, expect every campaign with a shot at winning to encourage its supporters to
bullet vote. "

Bullet voting can "backfire against one's top choice under Condorcet" because Condorcet
methods, unlike IRV, fail Later-no-Help.

http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf

In this 1996 Douglas Woodall paper, see "Election 6" and the accompanying discussion on
page 5/6 of the pdf (labelled on the paper as "Page 13").

Quoting again from your paper:
"As mentioned, every voting system is theoretically vulnerable to strategic manipulation, and IRV
is no exception. However, under IRV, there is no strategy that can increase the likelihood of
electing one's first choice beyond the opportunity offered by honest rankings. While there are
strategies for increasing the chances of less preferred candidates under IRV, like push-over,
they are counter-intuitive."

The Push-over strategy is certainly not limited to improving the chance of electing a "lower
[than first] choice". Say sincere is:

49: A 
27: B>A
24: C>B

B is the IRV winner, but if  4-21 (inclusive) of the A voters change to C or C>? then the winner
changes to A.

But as you say the strategy isn't "intuitive" , and backfires if too many of the A supporters try it.
Some IRV opponents claim to like Top-Two Runoff, but that is more vulnerable to Push-over
than IRV (because the strategists can support their sincere favourite in the second round).

The quite intuitive strategy that IRV is vulnerable to is Compromise, like any other method that
meets Majority. But voters' incentive to compromise (vote one's front-runner lesser-evil in first
place to reduce the chance of front-runner greater-evil winning) is generally vastly vastly less
than it is under FPP.

(There are methods that meet both Majority and Favourite Betrayal, and in them compromisers
can harmlessly vote their sincere favourites in equal-first place.)

But some Condorcet advocates are galled  by the Compromise incentive that can exist where
there is a sincere CW who is not also a sincere Mutual Dominant Third winner.

49: A>B
02: B>A
22: B
27: C>B

On these votes B is the CW, but IRV elects A.  If the C>B voters change to B then B will be
the voted majority favourite, so of course IRV like Condorcet methods and FPP will elect B.

Chris Benham

 
Greg wrote (Wed.Nov.19, 2008):
I have written up my reasons for preferring IRV over Condorcet methods
in an essay, the current draft of which is available here:
http://www.gregdennis.com/voting/irv_vs_condorcet.html

I welcome any comments you have.

Thanks,
Greg



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Juho Laatu
2008-11-20 20:49:26 UTC
Permalink
#1
- If your target is to elect Condorcet winners methods that meet Condorcet criterion could be considered.

#2
- There are also simple Condorcet methods like "elect the one that needs least additional votes to win all others".
- It is also a fact that in many countries few voters actually know and care about the internal details of the method. IRV and Condorcet may look quite similar to them.

#3
- I don't think _rational_and_successful_use_ of Condorcet strategies is intuitive to the regular voters.
- Some voters may however follow proposed strategies even if they are irrational (also in IRV).
- IRV has its problematic scenarios too (like you shortly mentioned).
- In large public elections with independent decision making, inaccurate poll information, changing opinions, and less than 100% penetration of strategic voters many strategic vulnerabilities of Condorcet become difficult to apply (or are not probable). Many strategies are easier to carry out on paper and with exaggerated votes and exaggerated voter behaviour than in real life. Each example should be analysed in detail but I'll skip that for now.

#4
- One simple approach for A and B would be to sling mud on C too. C seems to be a potential winner (maybe even a sincere Condorcet winner) so one should definitely not let him just hide (if mud is generally used).
- I think all candidates want all kind of support (core or other), also in Condorcet although only IRV requires strong core support.
- Hiding candidates may be seen as weak candidates, and therefore also Condorcet candidates need clear statements and a profile.
- Also in IRV candidates should try to please all the voters to get second preferences (they are important too although first preferences are a must).
- No big difference between candidate behaviour. In IRV candidates with limited first place support are not likely to be successful.

#5
- Yes, the methods could pave the way for each others. IRV leads in the U.S.. so it may help more.

#6
- I don't see a big difference between IRV+STV and Condorcet+STV. Ranking based single winner methods should be a good enough stepping stone for ranking based multi winner methods. Political will may be more important than the internal details of the methods.
(- Legal battles might be another thing, and that is a risk in the U.S.)
(- Also other good multi winner methods than STV exist.)

#7
- Yes, IRV seems to be ahead in the U.S.
- People may be familiar with runoffs, but also with tournaments


Many of the reasons didn't say that IRV is a better method than Condorcet but focused on other benefits of IRV (or on how it can help Condorcet). Strategic vulnerabilities seemed to be the central point when comparing the actual methods. The vulnerabilities of the two methods are different. I don't think Condorcet is essentially more vulnerable in typical public elections.

Also performance with sincere votes should have some weight. Electing a "wrong" candidate with sincere votes doesn't look nice. If election of Condorcet winners is the target then one could try to guarantee that.

In some places voters are happy to vote as told by strategists and use whatever tricks there might be. In some places strategic voting is not considered to be good behaviour. Also individuals are different. One could use methods with suitable resistance against strategies or methods that pick good winners depending on the expected strategic behaviour level of the environment. (One could also change the method to a better one if one sees that fears of widespread strategic voting did not materialize, or the other way around.)

IRV and Condorcet promoters could indeed cooperate more. IRV is not that bad, and Condorcet certainly neither. The disagreeing promoters (trying to kill the campaigns of each others) may actually be one of the biggest problems slowing down progress in the U.S. Condorcet has also the problem that it has different variants and no consensus on which one is the best.

The serial elimination process of IRV may be appealing to the voters (looks like a good fight where some super hero remains last) but due to its semi-random nature (see e.g. the Yee diagrams) it can't be considered to be optimal. IRV is however an improvement when compared to many methods in use today.

I tried to be brief. Ask for clarifications if I was too brief somewhere.

Juho
Subject: [EM] Why I Prefer IRV to Condorcet
Date: Wednesday, 19 November, 2008, 11:28 PM
I have written up my reasons for preferring IRV over
Condorcet methods
http://www.gregdennis.com/voting/irv_vs_condorcet.html
I welcome any comments you have.
Thanks,
Greg
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http://electorama.com/em for list info
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f***@pcc.edu
2008-11-21 20:35:43 UTC
Permalink
For some light on the question as to whether or not IRV's failures of the
Condorcet Criterion are apt to be rare:

http://zesty.ca/voting/sim/

FWS
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Greg Dennis
2008-11-21 23:56:04 UTC
Permalink
Thanks for the comments, Kevin. I'll try to offer some clarifications
below . . .
Post by Kevin Venzke
I want to comment on the first point/reason. I'll quote from the page.
First and foremost, IRV eliminates the most common type of Condorcet
failure --- the "spoiler" scenario --- where the presence of a candidate
with little core support causes a Condorcet winner with strong core
support to lose.
I don't understand what kind of scenario you're referring to. I thought I
did, and was going to say that good Condorcet methods don't behave in
that way. But then I noticed the term "core support," which puzzles me
in the context of Condorcet spoilers.
My poor wording lead you astray here. When I referred to "the most
common type of Condorcet failure," I did now mean the common common
way in which a Condorcet method fails. I meant the most common
violation of the Condorcet criterion that we see in elections today. I
am not saying anything about Condorcet methods in this paragraph. Both
IRV and Condorcet fix this spoiler problem. I'll improve the wording.
Post by Kevin Venzke
Admittedly, there is another situation similar to the spoiler problem ---
the "center squeeze" scenario -- in which IRV may fail to elect the
Condorcet winner. In this scenario, the presence of a candidate with
strong core support causes a Condorcet winner with little core support to
lose. Fortunately, despite the theoretical possibility of this scenario,
the empirical evidence suggests that it is vanishingly rare in practice.
Despite the hundreds of public IRV elections that are conducted worldwide
every year, the actual concrete examples of it occurring in practice are
few and far between.
A problem with using IRV elections to judge whether IRV suffers from
a center squeeze effect, is that it overlooks the possibility that IRV's
nomination incentives deter would-be Condorcet winners from running
(due to the fact that everyone knows they would not win).
A fair point. I don't see it in practice, though. In the recent San
Francisco IRV elections, for example, there were three open seats
(incumbents weren't running). Two of the seats saw 9 candidates
running, one saw 7. It seems that everyone and their brother is
throwing their hat in the ring of these IRV races, with no sign that
centrists are being deterred by the voting method. I think the reason
that centrists aren't deterred is that they have nothing to lose --
the entry of a centrist with weak core support can't throw the
election to a less preferred candidate under IRV. The worst that can
happen is they're eliminated in an early round and then the tallying
carries on as it would have had they not entered the race. With
plurality, we see a very obvious nomination incentive, with potential
spoiler candidates publicly and explicitly dropping out of races,
because of the impact they may have. I've yet to see or hear of
anything comparable in an IRV race.
Post by Kevin Venzke
You can make the argument that plurality also has very good Condorcet
efficiency since it is never observed to fail to elect a Condorcet winner.
Even adding the ability to rank lower preferences would probably not
change this, since with no real change to the method there is also no
real change to the nomination incentives.
While we don't have actual ranks to observe in plurality elections, we
still have pretty strong evidence, based on polling data, that
plurality has failed to elect the Condorcet winner in practice.
Post by Kevin Venzke
I have a few problems with #4... Partly that I find the arguments
speculative wrt candidate behavior, and partly that I don't see an
inherent advantage in knowing where candidates stand if everything is
still going to come down to competing blocs of core support that probably
dislike each other. Mostly, and related, it's that if we agree that we
can't trust voters to give us meaningful lower preferences, then I lose
most of my enthuasism for voting methods. If we can only trust first
preferences, and candidates that get a lot of first preferences, how much
room do we really have to make improvements? We can stray from plurality
hardly at all.
I trust lower preferences for candidates that exceed some threshold of
name recognition and exposure. That, for me, is where the benefit for
first preferences and "core support" come into play. They ensure the
candidate has at least some level of exposure.

Greg
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Kevin Venzke
2008-11-22 17:07:34 UTC
Permalink
Hi Greg,
Post by Greg Dennis
A fair point. I don't see it in practice, though. In
the recent San
Francisco IRV elections, for example, there were three open
seats
(incumbents weren't running). Two of the seats saw 9
candidates
running, one saw 7. It seems that everyone and their
brother is
throwing their hat in the ring of these IRV races, with no
sign that
centrists are being deterred by the voting method. I think
the reason
that centrists aren't deterred is that they have
nothing to lose --
the entry of a centrist with weak core support can't
throw the
election to a less preferred candidate under IRV. The worst
that can
happen is they're eliminated in an early round and then
the tallying
carries on as it would have had they not entered the race.
With
plurality, we see a very obvious nomination incentive, with
potential
spoiler candidates publicly and explicitly dropping out of
races,
because of the impact they may have. I've yet to see or
hear of
anything comparable in an IRV race.
Well, it seems to me there is a conflict in saying that centrists are not
deterred from running and yet IRV is not exhibiting the center squeeze
effect or violating Condorcet. It seems to me that these candidates either
shouldn't really be called centrists, or else they are centrists but don't
have the resources necessary to become visible, viable candidates (since
how are you going to get donations etc. if we can already say that you
won't win).

There may be something about San Francisco elections that I'm not aware
of.

Kevin Venzke



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Greg
2008-11-22 01:06:27 UTC
Permalink
Thanks, Chris. I'll correct the errors and rephrase some things I
didn't say correctly.

On the Compromise strategy, I think some compromises are more
intuitive than others. I think it's intuitive to abandon a more weakly
supported candidate, e.g. Nader, in favor of a major candidate, as is
common in FPTP. But it strikes me as more counter-intuitive, at least
for the average voter, to abandon a candidate with strong core support
in favor of a more weakly supported candidate, as could happen under
IRV. Then there's the issue as to whether the result of the
strategizing is a better or worse result overall . . . but that's a
tricky topic for another time.
Date: Thu, 20 Nov 2008 11:51:01 -0800 (PST)
Subject: [EM] Why I Prefer IRV to Condorcet
Greg,
I generally liked your essay. I rate IRV as the best of the single-winner methods that
meet Later-no-Harm, and a good method (and a vast improvement on FPP).
But I think you made a couple of technical errors.
"However, because bullet voting can help and never backfire against one's top choice under
Condorcet, expect every campaign with a shot at winning to encourage its supporters to
bullet vote. "
Bullet voting can "backfire against one's top choice under Condorcet" because Condorcet
methods, unlike IRV, fail Later-no-Help.
http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf
In this 1996 Douglas Woodall paper, see "Election 6" and the accompanying discussion on
page 5/6 of the pdf (labelled on the paper as "Page 13").
"As mentioned, every voting system is theoretically vulnerable to strategic manipulation, and IRV
is no exception. However, under IRV, there is no strategy that can increase the likelihood of
electing one's first choice beyond the opportunity offered by honest rankings. While there are
strategies for increasing the chances of less preferred candidates under IRV, like push-over,
they are counter-intuitive."
The Push-over strategy is certainly not limited to improving the chance of electing a "lower
49: A?
27: B>A
24: C>B
B is the IRV winner, but if? 4-21 (inclusive) of the A voters change to C or C>? then the winner
changes to A.
But as you say the strategy isn't "intuitive" , and backfires if too many of the A supporters try it.
Some IRV opponents claim to like Top-Two Runoff, but that is more vulnerable to Push-over
than IRV (because the strategists can support their sincere favourite in the second round).
The quite intuitive strategy that IRV is vulnerable to is Compromise, like any other method that
meets Majority. But voters' incentive to compromise (vote one's front-runner lesser-evil in first
place to reduce the chance of front-runner greater-evil winning) is generally vastly vastly less
than it is under FPP.
(There are methods that meet both Majority and Favourite Betrayal, and in them compromisers
can harmlessly vote their sincere favourites in equal-first place.)
But some Condorcet advocates are galled? by the Compromise incentive that can exist where
there is a sincere CW who is not also a sincere Mutual Dominant Third winner.
49: A>B
02: B>A
22: B
27: C>B
On these votes B is the CW, but IRV elects A.? If the C>B voters change to B then B will be
the voted majority favourite, so of course IRV like Condorcet methods and FPP will elect B.
Chris Benham
----
Election-Methods mailing list - see http://electorama.com/em for list info
Juho Laatu
2008-11-22 07:00:43 UTC
Permalink
Here's one IRV example with three strong candidates and where voters do have some incentive to compromise.

45: A>B>C
10: B>A>C
15: B>C>A
30: C>B>A

We have one centrist candidate (B) between two others.

According to this poll it seems that B will be eliminated first, and then A would win since some B supporters prefer A to C.

If sufficient number of C supporters would abandon their favourite and vote B>C>A, then C would be eliminated first and the centrist candidate B would be elected.

Based on this poll it seems that if C voters don't compromise (or if C will not withdraw) then from C supporters' point of view the worst candidate (A) will be elected.

- This situation could be reasonably common (or plausible) in real life
- B is a Condorcet winner ((that IRV would not elect))
- B seems to be politically closer to C than to A
- C is not a weak candidate since with few more "core" voters or second place support it could beat A (if the strong centrist candidate B will be eliminated first)

C supporters could be optimistic and hope for a change in opinions before the election day. I mean that in real elections many voters may be optimistic and fighting spirited and believe rather in those earlier polls that gave their favourite more votes than this poll etc.

The strategy of the C voters is not very "intuitive" in the sense that it is never natural to abandon one's favourite (it could be easier e.g. to rank the strongest competitor last even if that would be an irrational strategy). But on the other hand it is quite straight forward to see from the poll results (maybe voiced out by media) that indeed it makes sense for the C supporters to give up and abandon C if people will vote as indicated in this poll. The voters will thus have a dilemma, whether to vote sincerely or whether to compromise.

Juho
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Saturday, 22 November, 2008, 3:06 AM
Thanks, Chris. I'll correct the errors and rephrase some
things I
didn't say correctly.
On the Compromise strategy, I think some compromises are
more
intuitive than others. I think it's intuitive to
abandon a more weakly
supported candidate, e.g. Nader, in favor of a major
candidate, as is
common in FPTP. But it strikes me as more
counter-intuitive, at least
for the average voter, to abandon a candidate with strong
core support
in favor of a more weakly supported candidate, as could
happen under
IRV. Then there's the issue as to whether the result of
the
strategizing is a better or worse result overall . . . but
that's a
tricky topic for another time.
Date: Thu, 20 Nov 2008 11:51:01 -0800 (PST)
Subject: [EM] Why I Prefer IRV to Condorcet
Greg,
I generally liked your essay. I rate IRV as the best
of the single-winner methods that
meet Later-no-Harm, and a good method (and a vast
improvement on FPP).
But I think you made a couple of technical errors.
"However, because bullet voting can help and
never backfire against one's top choice under
Condorcet, expect every campaign with a shot at
winning to encourage its supporters to
bullet vote. "
Bullet voting can "backfire against one's top
choice under Condorcet" because Condorcet
methods, unlike IRV, fail Later-no-Help.
http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf
In this 1996 Douglas Woodall paper, see "Election
6" and the accompanying discussion on
page 5/6 of the pdf (labelled on the paper as
"Page 13").
"As mentioned, every voting system is
theoretically vulnerable to strategic manipulation, and IRV
is no exception. However, under IRV, there is no
strategy that can increase the likelihood of
electing one's first choice beyond the opportunity
offered by honest rankings. While there are
strategies for increasing the chances of less
preferred candidates under IRV, like push-over,
they are counter-intuitive."
The Push-over strategy is certainly not limited to
improving the chance of electing a "lower
49: A?
27: B>A
24: C>B
B is the IRV winner, but if? 4-21 (inclusive) of the A
voters change to C or C>? then the winner
changes to A.
But as you say the strategy isn't
"intuitive" , and backfires if too many of the A
supporters try it.
Some IRV opponents claim to like Top-Two Runoff, but
that is more vulnerable to Push-over
than IRV (because the strategists can support their
sincere favourite in the second round).
The quite intuitive strategy that IRV is vulnerable to
is Compromise, like any other method that
meets Majority. But voters' incentive to
compromise (vote one's front-runner lesser-evil in first
place to reduce the chance of front-runner
greater-evil winning) is generally vastly vastly less
than it is under FPP.
(There are methods that meet both Majority and
Favourite Betrayal, and in them compromisers
can harmlessly vote their sincere favourites in
equal-first place.)
But some Condorcet advocates are galled? by the
Compromise incentive that can exist where
there is a sincere CW who is not also a sincere Mutual
Dominant Third winner.
49: A>B
02: B>A
22: B
27: C>B
On these votes B is the CW, but IRV elects A.? If the
C>B voters change to B then B will be
the voted majority favourite, so of course IRV like
Condorcet methods and FPP will elect B.
Chris Benham
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Election-Methods mailing list - see
http://electorama.com/em for list info
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Greg
2008-11-22 08:04:42 UTC
Permalink
Yes, this is as intuitive as it comes in terms of IRV strategy, but I
still find it ultimately counter-intuitive for the average voter.
Candidate C has a the second-most number of first choices, which
likely corresponds to the second-biggest campaign (second-most amount
of money, volunteers, name recognition, exposure, ads, etc). The
thought of abandoning C in favor of B, who will probably have a
smaller campaign (less money, fewer volunteers, etc), I think will
strike the average voter as counter-intuitive. In these respects, this
scenario is quite unlike the standard spoiler scenario, where the
incentive is to intuitively switch one's vote from the smaller to the
bigger campaign. Nevertheless, I would agree that it's something to be
on the lookout for as IRV spreads.

Greg
Post by Juho Laatu
Here's one IRV example with three strong candidates and where voters do have some incentive to compromise.
45: A>B>C
10: B>A>C
15: B>C>A
30: C>B>A
We have one centrist candidate (B) between two others.
According to this poll it seems that B will be eliminated first, and then A would win since some B supporters prefer A to C.
If sufficient number of C supporters would abandon their favourite and vote B>C>A, then C would be eliminated first and the centrist candidate B would be elected.
Based on this poll it seems that if C voters don't compromise (or if C will not withdraw) then from C supporters' point of view the worst candidate (A) will be elected.
- This situation could be reasonably common (or plausible) in real life
- B is a Condorcet winner ((that IRV would not elect))
- B seems to be politically closer to C than to A
- C is not a weak candidate since with few more "core" voters or second place support it could beat A (if the strong centrist candidate B will be eliminated first)
C supporters could be optimistic and hope for a change in opinions before the election day. I mean that in real elections many voters may be optimistic and fighting spirited and believe rather in those earlier polls that gave their favourite more votes than this poll etc.
The strategy of the C voters is not very "intuitive" in the sense that it is never natural to abandon one's favourite (it could be easier e.g. to rank the strongest competitor last even if that would be an irrational strategy). But on the other hand it is quite straight forward to see from the poll results (maybe voiced out by media) that indeed it makes sense for the C supporters to give up and abandon C if people will vote as indicated in this poll. The voters will thus have a dilemma, whether to vote sincerely or whether to compromise.
Juho
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Saturday, 22 November, 2008, 3:06 AM
Thanks, Chris. I'll correct the errors and rephrase some
things I
didn't say correctly.
On the Compromise strategy, I think some compromises are
more
intuitive than others. I think it's intuitive to
abandon a more weakly
supported candidate, e.g. Nader, in favor of a major
candidate, as is
common in FPTP. But it strikes me as more
counter-intuitive, at least
for the average voter, to abandon a candidate with strong
core support
in favor of a more weakly supported candidate, as could
happen under
IRV. Then there's the issue as to whether the result of
the
strategizing is a better or worse result overall . . . but
that's a
tricky topic for another time.
Date: Thu, 20 Nov 2008 11:51:01 -0800 (PST)
Subject: [EM] Why I Prefer IRV to Condorcet
Greg,
I generally liked your essay. I rate IRV as the best
of the single-winner methods that
meet Later-no-Harm, and a good method (and a vast
improvement on FPP).
But I think you made a couple of technical errors.
"However, because bullet voting can help and
never backfire against one's top choice under
Condorcet, expect every campaign with a shot at
winning to encourage its supporters to
bullet vote. "
Bullet voting can "backfire against one's top
choice under Condorcet" because Condorcet
methods, unlike IRV, fail Later-no-Help.
http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf
In this 1996 Douglas Woodall paper, see "Election
6" and the accompanying discussion on
page 5/6 of the pdf (labelled on the paper as
"Page 13").
"As mentioned, every voting system is
theoretically vulnerable to strategic manipulation, and IRV
is no exception. However, under IRV, there is no
strategy that can increase the likelihood of
electing one's first choice beyond the opportunity
offered by honest rankings. While there are
strategies for increasing the chances of less
preferred candidates under IRV, like push-over,
they are counter-intuitive."
The Push-over strategy is certainly not limited to
improving the chance of electing a "lower
49: A?
27: B>A
24: C>B
B is the IRV winner, but if? 4-21 (inclusive) of the A
voters change to C or C>? then the winner
changes to A.
But as you say the strategy isn't
"intuitive" , and backfires if too many of the A
supporters try it.
Some IRV opponents claim to like Top-Two Runoff, but
that is more vulnerable to Push-over
than IRV (because the strategists can support their
sincere favourite in the second round).
The quite intuitive strategy that IRV is vulnerable to
is Compromise, like any other method that
meets Majority. But voters' incentive to
compromise (vote one's front-runner lesser-evil in first
place to reduce the chance of front-runner
greater-evil winning) is generally vastly vastly less
than it is under FPP.
(There are methods that meet both Majority and
Favourite Betrayal, and in them compromisers
can harmlessly vote their sincere favourites in
equal-first place.)
But some Condorcet advocates are galled? by the
Compromise incentive that can exist where
there is a sincere CW who is not also a sincere Mutual
Dominant Third winner.
49: A>B
02: B>A
22: B
27: C>B
On these votes B is the CW, but IRV elects A.? If the
C>B voters change to B then B will be
the voted majority favourite, so of course IRV like
Condorcet methods and FPP will elect B.
Chris Benham
----
Election-Methods mailing list - see
http://electorama.com/em for list info
----
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Juho Laatu
2008-11-22 10:53:24 UTC
Permalink
Yes, it is not intuitive to abandon one's favourite. What is then intuitive? Burying as a Condorcet strategy is certainly not intuitive (quite difficult to understand even to experts). Burying in the sense of ranking the strongest competitor of one's favourite potential winner last may be intuitive to many.

Since in Condorcet there are some situations where burying is a working strategy, this property (if advertised) may encourage people to (irrationally) bury (or rank the competitors last) even more generally. In IRV voters may also intuitively bury although that doesn't make much sense.

In Condorcet one would thus have to trust "political advisers" to tell when to bury (to make the strategy rational). Similarly in the example that I gave the voters would maybe have to be reminded that it could be wise to compromise this time.



Although all the three factions are large the B supporters may see C as a spoiler. If C would not participate both B and C supporters would be happier with the outcome. (C thus spoils the result also from the C supporters' point of view.)

In the example B and C could be candidates of the same party. Then nominating also C (the more extreme of the two potential candidates) was maybe a mistake.

Juho
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Saturday, 22 November, 2008, 10:04 AM
Yes, this is as intuitive as it comes in terms of IRV
strategy, but I
still find it ultimately counter-intuitive for the average
voter.
Candidate C has a the second-most number of first choices,
which
likely corresponds to the second-biggest campaign
(second-most amount
of money, volunteers, name recognition, exposure, ads,
etc). The
thought of abandoning C in favor of B, who will probably
have a
smaller campaign (less money, fewer volunteers, etc), I
think will
strike the average voter as counter-intuitive. In these
respects, this
scenario is quite unlike the standard spoiler scenario,
where the
incentive is to intuitively switch one's vote from the
smaller to the
bigger campaign. Nevertheless, I would agree that it's
something to be
on the lookout for as IRV spreads.
Greg
On Sat, Nov 22, 2008 at 2:00 AM, Juho Laatu
Post by Juho Laatu
Here's one IRV example with three strong
candidates and where voters do have some incentive to
compromise.
Post by Juho Laatu
45: A>B>C
10: B>A>C
15: B>C>A
30: C>B>A
We have one centrist candidate (B) between two others.
According to this poll it seems that B will be
eliminated first, and then A would win since some B
supporters prefer A to C.
Post by Juho Laatu
If sufficient number of C supporters would abandon
their favourite and vote B>C>A, then C would be
eliminated first and the centrist candidate B would be
elected.
Post by Juho Laatu
Based on this poll it seems that if C voters don't
compromise (or if C will not withdraw) then from C
supporters' point of view the worst candidate (A) will
be elected.
Post by Juho Laatu
- This situation could be reasonably common (or
plausible) in real life
Post by Juho Laatu
- B is a Condorcet winner ((that IRV would not elect))
- B seems to be politically closer to C than to A
- C is not a weak candidate since with few more
"core" voters or second place support it could
beat A (if the strong centrist candidate B will be
eliminated first)
Post by Juho Laatu
C supporters could be optimistic and hope for a change
in opinions before the election day. I mean that in real
elections many voters may be optimistic and fighting
spirited and believe rather in those earlier polls that gave
their favourite more votes than this poll etc.
Post by Juho Laatu
The strategy of the C voters is not very
"intuitive" in the sense that it is never natural
to abandon one's favourite (it could be easier e.g. to
rank the strongest competitor last even if that would be an
irrational strategy). But on the other hand it is quite
straight forward to see from the poll results (maybe voiced
out by media) that indeed it makes sense for the C
supporters to give up and abandon C if people will vote as
indicated in this poll. The voters will thus have a dilemma,
whether to vote sincerely or whether to compromise.
Post by Juho Laatu
Juho
--- On Sat, 22/11/08, Greg
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Saturday, 22 November, 2008, 3:06 AM
Thanks, Chris. I'll correct the errors and
rephrase some
Post by Juho Laatu
things I
didn't say correctly.
On the Compromise strategy, I think some
compromises are
Post by Juho Laatu
more
intuitive than others. I think it's intuitive
to
Post by Juho Laatu
abandon a more weakly
supported candidate, e.g. Nader, in favor of a
major
Post by Juho Laatu
candidate, as is
common in FPTP. But it strikes me as more
counter-intuitive, at least
for the average voter, to abandon a candidate with
strong
Post by Juho Laatu
core support
in favor of a more weakly supported candidate, as
could
Post by Juho Laatu
happen under
IRV. Then there's the issue as to whether the
result of
Post by Juho Laatu
the
strategizing is a better or worse result overall .
. . but
Post by Juho Laatu
that's a
tricky topic for another time.
Date: Thu, 20 Nov 2008 11:51:01 -0800 (PST)
From: Chris Benham
Subject: [EM] Why I Prefer IRV to Condorcet
Greg,
I generally liked your essay. I rate IRV as
the best
Post by Juho Laatu
of the single-winner methods that
meet Later-no-Harm, and a good method (and a
vast
Post by Juho Laatu
improvement on FPP).
But I think you made a couple of technical
errors.
Post by Juho Laatu
"However, because bullet voting can help
and
Post by Juho Laatu
never backfire against one's top choice under
Condorcet, expect every campaign with a shot
at
Post by Juho Laatu
winning to encourage its supporters to
bullet vote. "
Bullet voting can "backfire against
one's top
Post by Juho Laatu
choice under Condorcet" because Condorcet
methods, unlike IRV, fail Later-no-Help.
http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf
Post by Juho Laatu
In this 1996 Douglas Woodall paper, see
"Election
Post by Juho Laatu
6" and the accompanying discussion on
page 5/6 of the pdf (labelled on the paper as
"Page 13").
"As mentioned, every voting system is
theoretically vulnerable to strategic
manipulation, and IRV
Post by Juho Laatu
is no exception. However, under IRV, there is
no
Post by Juho Laatu
strategy that can increase the likelihood of
electing one's first choice beyond the
opportunity
Post by Juho Laatu
offered by honest rankings. While there are
strategies for increasing the chances of less
preferred candidates under IRV, like push-over,
they are counter-intuitive."
The Push-over strategy is certainly not
limited to
Post by Juho Laatu
improving the chance of electing a "lower
49: A?
27: B>A
24: C>B
B is the IRV winner, but if? 4-21 (inclusive)
of the A
Post by Juho Laatu
voters change to C or C>? then the winner
changes to A.
But as you say the strategy isn't
"intuitive" , and backfires if too many
of the A
Post by Juho Laatu
supporters try it.
Some IRV opponents claim to like Top-Two
Runoff, but
Post by Juho Laatu
that is more vulnerable to Push-over
than IRV (because the strategists can support
their
Post by Juho Laatu
sincere favourite in the second round).
The quite intuitive strategy that IRV is
vulnerable to
Post by Juho Laatu
is Compromise, like any other method that
meets Majority. But voters' incentive to
compromise (vote one's front-runner
lesser-evil in first
Post by Juho Laatu
place to reduce the chance of front-runner
greater-evil winning) is generally vastly vastly
less
Post by Juho Laatu
than it is under FPP.
(There are methods that meet both Majority
and
Post by Juho Laatu
Favourite Betrayal, and in them compromisers
can harmlessly vote their sincere favourites
in
Post by Juho Laatu
equal-first place.)
But some Condorcet advocates are galled? by
the
Post by Juho Laatu
Compromise incentive that can exist where
there is a sincere CW who is not also a
sincere Mutual
Post by Juho Laatu
Dominant Third winner.
49: A>B
02: B>A
22: B
27: C>B
On these votes B is the CW, but IRV elects
A.? If the
Post by Juho Laatu
C>B voters change to B then B will be
the voted majority favourite, so of course
IRV like
Post by Juho Laatu
Condorcet methods and FPP will elect B.
Chris Benham
----
Election-Methods mailing list - see
http://electorama.com/em for list info
----
Election-Methods mailing list - see http://electorama.com/em for list info
Greg
2008-11-22 18:02:17 UTC
Permalink
Perhaps intuitiveness is a bit in the eyes of the beholder, but I'll
tell you the strategies I find intuitive:

- Burying a candidate with strong first choice support
- Bullet voting for a candidate with strong first choice support
- A compromise in which you switch your first choice vote to a
candidate who has stronger first choice support.
From anecdotal personal experience, I actually think burying might be
the most intuitive of them all. Almost every university election I
voted for as an undergraduate used IRV. After each one, there was
often a person here or there who claimed to have voted for one
front-runner and buried the other front-runner on their ballot, not
aware that this had no effect on the outcome. Now, as I go around
teaching IRV to people, there's often some guy who thinks he's clever
who brings up the idea of burying (though he doesn't know the term
"bury"), thinking he's discovered some sort of flaw; that is, until I
correct him.

It is from this personal experience that I have grown to believe
resistance to burying essential. Again, this is purely anecdotal, and
empirical research in this area would be helpful.

Greg
Yes, it is not intuitive to abandon one's favourite. What is then intuitive? Burying as a Condorcet strategy is certainly not intuitive (quite difficult to understand even to experts). Burying in the sense of ranking the strongest competitor of one's favourite potential winner last may be intuitive to many.
Since in Condorcet there are some situations where burying is a working strategy, this property (if advertised) may encourage people to (irrationally) bury (or rank the competitors last) even more generally. In IRV voters may also intuitively bury although that doesn't make much sense.
In Condorcet one would thus have to trust "political advisers" to tell when to bury (to make the strategy rational). Similarly in the example that I gave the voters would maybe have to be reminded that it could be wise to compromise this time.
Although all the three factions are large the B supporters may see C as a spoiler. If C would not participate both B and C supporters would be happier with the outcome. (C thus spoils the result also from the C supporters' point of view.)
In the example B and C could be candidates of the same party. Then nominating also C (the more extreme of the two potential candidates) was maybe a mistake.
Juho
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Saturday, 22 November, 2008, 10:04 AM
Yes, this is as intuitive as it comes in terms of IRV
strategy, but I
still find it ultimately counter-intuitive for the average
voter.
Candidate C has a the second-most number of first choices,
which
likely corresponds to the second-biggest campaign
(second-most amount
of money, volunteers, name recognition, exposure, ads,
etc). The
thought of abandoning C in favor of B, who will probably
have a
smaller campaign (less money, fewer volunteers, etc), I
think will
strike the average voter as counter-intuitive. In these
respects, this
scenario is quite unlike the standard spoiler scenario,
where the
incentive is to intuitively switch one's vote from the
smaller to the
bigger campaign. Nevertheless, I would agree that it's
something to be
on the lookout for as IRV spreads.
Greg
On Sat, Nov 22, 2008 at 2:00 AM, Juho Laatu
Post by Juho Laatu
Here's one IRV example with three strong
candidates and where voters do have some incentive to
compromise.
Post by Juho Laatu
45: A>B>C
10: B>A>C
15: B>C>A
30: C>B>A
We have one centrist candidate (B) between two others.
According to this poll it seems that B will be
eliminated first, and then A would win since some B
supporters prefer A to C.
Post by Juho Laatu
If sufficient number of C supporters would abandon
their favourite and vote B>C>A, then C would be
eliminated first and the centrist candidate B would be
elected.
Post by Juho Laatu
Based on this poll it seems that if C voters don't
compromise (or if C will not withdraw) then from C
supporters' point of view the worst candidate (A) will
be elected.
Post by Juho Laatu
- This situation could be reasonably common (or
plausible) in real life
Post by Juho Laatu
- B is a Condorcet winner ((that IRV would not elect))
- B seems to be politically closer to C than to A
- C is not a weak candidate since with few more
"core" voters or second place support it could
beat A (if the strong centrist candidate B will be
eliminated first)
Post by Juho Laatu
C supporters could be optimistic and hope for a change
in opinions before the election day. I mean that in real
elections many voters may be optimistic and fighting
spirited and believe rather in those earlier polls that gave
their favourite more votes than this poll etc.
Post by Juho Laatu
The strategy of the C voters is not very
"intuitive" in the sense that it is never natural
to abandon one's favourite (it could be easier e.g. to
rank the strongest competitor last even if that would be an
irrational strategy). But on the other hand it is quite
straight forward to see from the poll results (maybe voiced
out by media) that indeed it makes sense for the C
supporters to give up and abandon C if people will vote as
indicated in this poll. The voters will thus have a dilemma,
whether to vote sincerely or whether to compromise.
Post by Juho Laatu
Juho
--- On Sat, 22/11/08, Greg
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Saturday, 22 November, 2008, 3:06 AM
Thanks, Chris. I'll correct the errors and
rephrase some
Post by Juho Laatu
things I
didn't say correctly.
On the Compromise strategy, I think some
compromises are
Post by Juho Laatu
more
intuitive than others. I think it's intuitive
to
Post by Juho Laatu
abandon a more weakly
supported candidate, e.g. Nader, in favor of a
major
Post by Juho Laatu
candidate, as is
common in FPTP. But it strikes me as more
counter-intuitive, at least
for the average voter, to abandon a candidate with
strong
Post by Juho Laatu
core support
in favor of a more weakly supported candidate, as
could
Post by Juho Laatu
happen under
IRV. Then there's the issue as to whether the
result of
Post by Juho Laatu
the
strategizing is a better or worse result overall .
. . but
Post by Juho Laatu
that's a
tricky topic for another time.
Date: Thu, 20 Nov 2008 11:51:01 -0800 (PST)
From: Chris Benham
Subject: [EM] Why I Prefer IRV to Condorcet
Greg,
I generally liked your essay. I rate IRV as
the best
Post by Juho Laatu
of the single-winner methods that
meet Later-no-Harm, and a good method (and a
vast
Post by Juho Laatu
improvement on FPP).
But I think you made a couple of technical
errors.
Post by Juho Laatu
"However, because bullet voting can help
and
Post by Juho Laatu
never backfire against one's top choice under
Condorcet, expect every campaign with a shot
at
Post by Juho Laatu
winning to encourage its supporters to
bullet vote. "
Bullet voting can "backfire against
one's top
Post by Juho Laatu
choice under Condorcet" because Condorcet
methods, unlike IRV, fail Later-no-Help.
http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf
Post by Juho Laatu
In this 1996 Douglas Woodall paper, see
"Election
Post by Juho Laatu
6" and the accompanying discussion on
page 5/6 of the pdf (labelled on the paper as
"Page 13").
"As mentioned, every voting system is
theoretically vulnerable to strategic
manipulation, and IRV
Post by Juho Laatu
is no exception. However, under IRV, there is
no
Post by Juho Laatu
strategy that can increase the likelihood of
electing one's first choice beyond the
opportunity
Post by Juho Laatu
offered by honest rankings. While there are
strategies for increasing the chances of less
preferred candidates under IRV, like push-over,
they are counter-intuitive."
The Push-over strategy is certainly not
limited to
Post by Juho Laatu
improving the chance of electing a "lower
49: A?
27: B>A
24: C>B
B is the IRV winner, but if? 4-21 (inclusive)
of the A
Post by Juho Laatu
voters change to C or C>? then the winner
changes to A.
But as you say the strategy isn't
"intuitive" , and backfires if too many
of the A
Post by Juho Laatu
supporters try it.
Some IRV opponents claim to like Top-Two
Runoff, but
Post by Juho Laatu
that is more vulnerable to Push-over
than IRV (because the strategists can support
their
Post by Juho Laatu
sincere favourite in the second round).
The quite intuitive strategy that IRV is
vulnerable to
Post by Juho Laatu
is Compromise, like any other method that
meets Majority. But voters' incentive to
compromise (vote one's front-runner
lesser-evil in first
Post by Juho Laatu
place to reduce the chance of front-runner
greater-evil winning) is generally vastly vastly
less
Post by Juho Laatu
than it is under FPP.
(There are methods that meet both Majority
and
Post by Juho Laatu
Favourite Betrayal, and in them compromisers
can harmlessly vote their sincere favourites
in
Post by Juho Laatu
equal-first place.)
But some Condorcet advocates are galled? by
the
Post by Juho Laatu
Compromise incentive that can exist where
there is a sincere CW who is not also a
sincere Mutual
Post by Juho Laatu
Dominant Third winner.
49: A>B
02: B>A
22: B
27: C>B
On these votes B is the CW, but IRV elects
A.? If the
Post by Juho Laatu
C>B voters change to B then B will be
the voted majority favourite, so of course
IRV like
Post by Juho Laatu
Condorcet methods and FPP will elect B.
Chris Benham
----
Election-Methods mailing list - see
http://electorama.com/em for list info
----
Election-Methods mailing list - see http://electorama.com/em for list info
Juho Laatu
2008-11-22 19:50:06 UTC
Permalink
Post by Greg
Perhaps intuitiveness is a bit in the eyes of the beholder,
but I'll
- Burying a candidate with strong first choice support
Yes. This is close to the case that I discussed.
I didn't assume strong first choice support but
just any strength (e.g. being close to a Condorcet
winner).
Post by Greg
- Bullet voting for a candidate with strong first choice
support
Yes. (Also any other strength ok, or one could
bullet vote one's own not-so-strong favourite.)
Post by Greg
- A compromise in which you switch your first choice vote
to a
candidate who has stronger first choice support.
Yes. (Again strong first choice support typical
but not necessary.)
Post by Greg
From anecdotal personal experience, I actually think
burying might be
the most intuitive of them all.
Yes, may be.
Post by Greg
Almost every university
election I
voted for as an undergraduate used IRV. After each one,
there was
often a person here or there who claimed to have voted for
one
front-runner and buried the other front-runner on their
ballot, not
aware that this had no effect on the outcome. Now, as I go
around
teaching IRV to people, there's often some guy who
thinks he's clever
who brings up the idea of burying (though he doesn't
know the term
"bury"), thinking he's discovered some sort
of flaw; that is, until I
correct him.
One problem (or actually a good thing) with
strategies is that if there are strategies they
may not always be rational. In such a situation
hopefully we can recommend sincere voting to
all voters as a better alternative to confused
use of various strategies.
Post by Greg
It is from this personal experience that I have grown to
believe
resistance to burying essential. Again, this is purely
anecdotal, and
empirical research in this area would be helpful.
It is very difficult to defend against widespread
irrational use of strategies. Recommending sincere
voting may be a good approach. (Maybe people will
learn after spoiling some election and electing
some clearly unwanted candidate as a result of
burying all the reasonable competitors :-) .)

Juho
Post by Greg
Greg
On Sat, Nov 22, 2008 at 5:53 AM, Juho Laatu
Post by Juho Laatu
Yes, it is not intuitive to abandon one's
favourite. What is then intuitive? Burying as a Condorcet
strategy is certainly not intuitive (quite difficult to
understand even to experts). Burying in the sense of ranking
the strongest competitor of one's favourite potential
winner last may be intuitive to many.
Post by Juho Laatu
Since in Condorcet there are some situations where
burying is a working strategy, this property (if advertised)
may encourage people to (irrationally) bury (or rank the
competitors last) even more generally. In IRV voters may
also intuitively bury although that doesn't make much
sense.
Post by Juho Laatu
In Condorcet one would thus have to trust
"political advisers" to tell when to bury (to make
the strategy rational). Similarly in the example that I gave
the voters would maybe have to be reminded that it could be
wise to compromise this time.
Post by Juho Laatu
Although all the three factions are large the B
supporters may see C as a spoiler. If C would not
participate both B and C supporters would be happier with
the outcome. (C thus spoils the result also from the C
supporters' point of view.)
Post by Juho Laatu
In the example B and C could be candidates of the same
party. Then nominating also C (the more extreme of the two
potential candidates) was maybe a mistake.
Post by Juho Laatu
Juho
--- On Sat, 22/11/08, Greg
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Saturday, 22 November, 2008, 10:04 AM
Yes, this is as intuitive as it comes in terms of
IRV
Post by Juho Laatu
strategy, but I
still find it ultimately counter-intuitive for the
average
Post by Juho Laatu
voter.
Candidate C has a the second-most number of first
choices,
Post by Juho Laatu
which
likely corresponds to the second-biggest campaign
(second-most amount
of money, volunteers, name recognition, exposure,
ads,
Post by Juho Laatu
etc). The
thought of abandoning C in favor of B, who will
probably
Post by Juho Laatu
have a
smaller campaign (less money, fewer volunteers,
etc), I
Post by Juho Laatu
think will
strike the average voter as counter-intuitive. In
these
Post by Juho Laatu
respects, this
scenario is quite unlike the standard spoiler
scenario,
Post by Juho Laatu
where the
incentive is to intuitively switch one's vote
from the
Post by Juho Laatu
smaller to the
bigger campaign. Nevertheless, I would agree that
it's
Post by Juho Laatu
something to be
on the lookout for as IRV spreads.
Greg
On Sat, Nov 22, 2008 at 2:00 AM, Juho Laatu
Post by Juho Laatu
Here's one IRV example with three strong
candidates and where voters do have some incentive
to
Post by Juho Laatu
compromise.
Post by Juho Laatu
45: A>B>C
10: B>A>C
15: B>C>A
30: C>B>A
We have one centrist candidate (B) between
two others.
Post by Juho Laatu
Post by Juho Laatu
According to this poll it seems that B will
be
Post by Juho Laatu
eliminated first, and then A would win since some
B
Post by Juho Laatu
supporters prefer A to C.
Post by Juho Laatu
If sufficient number of C supporters would
abandon
Post by Juho Laatu
their favourite and vote B>C>A, then C would
be
Post by Juho Laatu
eliminated first and the centrist candidate B
would be
Post by Juho Laatu
elected.
Post by Juho Laatu
Based on this poll it seems that if C voters
don't
Post by Juho Laatu
compromise (or if C will not withdraw) then from C
supporters' point of view the worst candidate
(A) will
Post by Juho Laatu
be elected.
Post by Juho Laatu
- This situation could be reasonably common
(or
Post by Juho Laatu
plausible) in real life
Post by Juho Laatu
- B is a Condorcet winner ((that IRV would
not elect))
Post by Juho Laatu
Post by Juho Laatu
- B seems to be politically closer to C than
to A
Post by Juho Laatu
Post by Juho Laatu
- C is not a weak candidate since with few
more
Post by Juho Laatu
"core" voters or second place support it
could
Post by Juho Laatu
beat A (if the strong centrist candidate B will be
eliminated first)
Post by Juho Laatu
C supporters could be optimistic and hope for
a change
Post by Juho Laatu
in opinions before the election day. I mean that
in real
Post by Juho Laatu
elections many voters may be optimistic and
fighting
Post by Juho Laatu
spirited and believe rather in those earlier polls
that gave
Post by Juho Laatu
their favourite more votes than this poll etc.
Post by Juho Laatu
The strategy of the C voters is not very
"intuitive" in the sense that it is
never natural
Post by Juho Laatu
to abandon one's favourite (it could be easier
e.g. to
Post by Juho Laatu
rank the strongest competitor last even if that
would be an
Post by Juho Laatu
irrational strategy). But on the other hand it is
quite
Post by Juho Laatu
straight forward to see from the poll results
(maybe voiced
Post by Juho Laatu
out by media) that indeed it makes sense for the C
supporters to give up and abandon C if people will
vote as
Post by Juho Laatu
indicated in this poll. The voters will thus have
a dilemma,
Post by Juho Laatu
whether to vote sincerely or whether to
compromise.
Post by Juho Laatu
Post by Juho Laatu
Juho
--- On Sat, 22/11/08, Greg
Subject: Re: [EM] Why I Prefer IRV to
Condorcet
Post by Juho Laatu
Post by Juho Laatu
Date: Saturday, 22 November, 2008, 3:06
AM
Post by Juho Laatu
Post by Juho Laatu
Thanks, Chris. I'll correct the
errors and
Post by Juho Laatu
rephrase some
Post by Juho Laatu
things I
didn't say correctly.
On the Compromise strategy, I think some
compromises are
Post by Juho Laatu
more
intuitive than others. I think it's
intuitive
Post by Juho Laatu
to
Post by Juho Laatu
abandon a more weakly
supported candidate, e.g. Nader, in favor
of a
Post by Juho Laatu
major
Post by Juho Laatu
candidate, as is
common in FPTP. But it strikes me as more
counter-intuitive, at least
for the average voter, to abandon a
candidate with
Post by Juho Laatu
strong
Post by Juho Laatu
core support
in favor of a more weakly supported
candidate, as
Post by Juho Laatu
could
Post by Juho Laatu
happen under
IRV. Then there's the issue as to
whether the
Post by Juho Laatu
result of
Post by Juho Laatu
the
strategizing is a better or worse result
overall .
Post by Juho Laatu
. . but
Post by Juho Laatu
that's a
tricky topic for another time.
Date: Thu, 20 Nov 2008 11:51:01
-0800 (PST)
Post by Juho Laatu
Post by Juho Laatu
From: Chris Benham
Subject: [EM] Why I Prefer IRV to
Condorcet
Post by Juho Laatu
Post by Juho Laatu
Greg,
I generally liked your essay. I rate
IRV as
Post by Juho Laatu
the best
Post by Juho Laatu
of the single-winner methods that
meet Later-no-Harm, and a good
method (and a
Post by Juho Laatu
vast
Post by Juho Laatu
improvement on FPP).
But I think you made a couple of
technical
Post by Juho Laatu
errors.
Post by Juho Laatu
"However, because bullet voting
can help
Post by Juho Laatu
and
Post by Juho Laatu
never backfire against one's top
choice under
Post by Juho Laatu
Post by Juho Laatu
Condorcet, expect every campaign
with a shot
Post by Juho Laatu
at
Post by Juho Laatu
winning to encourage its supporters to
bullet vote. "
Bullet voting can "backfire
against
Post by Juho Laatu
one's top
Post by Juho Laatu
choice under Condorcet" because
Condorcet
Post by Juho Laatu
Post by Juho Laatu
methods, unlike IRV, fail
Later-no-Help.
http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf
Post by Juho Laatu
Post by Juho Laatu
In this 1996 Douglas Woodall paper,
see
Post by Juho Laatu
"Election
Post by Juho Laatu
6" and the accompanying discussion
on
Post by Juho Laatu
Post by Juho Laatu
page 5/6 of the pdf (labelled on the
paper as
Post by Juho Laatu
Post by Juho Laatu
"Page 13").
"As mentioned, every voting
system is
Post by Juho Laatu
Post by Juho Laatu
theoretically vulnerable to strategic
manipulation, and IRV
Post by Juho Laatu
is no exception. However, under IRV,
there is
Post by Juho Laatu
no
Post by Juho Laatu
strategy that can increase the likelihood
of
Post by Juho Laatu
Post by Juho Laatu
electing one's first choice
beyond the
Post by Juho Laatu
opportunity
Post by Juho Laatu
offered by honest rankings. While there
are
Post by Juho Laatu
Post by Juho Laatu
strategies for increasing the
chances of less
Post by Juho Laatu
Post by Juho Laatu
preferred candidates under IRV, like
push-over,
Post by Juho Laatu
Post by Juho Laatu
they are counter-intuitive."
The Push-over strategy is certainly
not
Post by Juho Laatu
limited to
Post by Juho Laatu
improving the chance of electing a
"lower
Post by Juho Laatu
Post by Juho Laatu
[than first] choice". Say
49: A?
27: B>A
24: C>B
B is the IRV winner, but if? 4-21
(inclusive)
Post by Juho Laatu
of the A
Post by Juho Laatu
voters change to C or C>? then the
winner
Post by Juho Laatu
Post by Juho Laatu
changes to A.
But as you say the strategy
isn't
Post by Juho Laatu
Post by Juho Laatu
"intuitive" , and backfires if
too many
Post by Juho Laatu
of the A
Post by Juho Laatu
supporters try it.
Some IRV opponents claim to like
Top-Two
Post by Juho Laatu
Runoff, but
Post by Juho Laatu
that is more vulnerable to Push-over
than IRV (because the strategists
can support
Post by Juho Laatu
their
Post by Juho Laatu
sincere favourite in the second round).
The quite intuitive strategy that
IRV is
Post by Juho Laatu
vulnerable to
Post by Juho Laatu
is Compromise, like any other method that
meets Majority. But voters'
incentive to
Post by Juho Laatu
Post by Juho Laatu
compromise (vote one's front-runner
lesser-evil in first
Post by Juho Laatu
place to reduce the chance of
front-runner
Post by Juho Laatu
Post by Juho Laatu
greater-evil winning) is generally vastly
vastly
Post by Juho Laatu
less
Post by Juho Laatu
than it is under FPP.
(There are methods that meet both
Majority
Post by Juho Laatu
and
Post by Juho Laatu
Favourite Betrayal, and in them
compromisers
Post by Juho Laatu
Post by Juho Laatu
can harmlessly vote their sincere
favourites
Post by Juho Laatu
in
Post by Juho Laatu
equal-first place.)
But some Condorcet advocates are
galled? by
Post by Juho Laatu
the
Post by Juho Laatu
Compromise incentive that can exist where
there is a sincere CW who is not
also a
Post by Juho Laatu
sincere Mutual
Post by Juho Laatu
Dominant Third winner.
49: A>B
02: B>A
22: B
27: C>B
On these votes B is the CW, but IRV
elects
Post by Juho Laatu
A.? If the
Post by Juho Laatu
C>B voters change to B then B will be
the voted majority favourite, so of
course
Post by Juho Laatu
IRV like
Post by Juho Laatu
Condorcet methods and FPP will elect B.
Chris Benham
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Jonathan Lundell
2008-11-22 18:01:26 UTC
Permalink
Post by Juho Laatu
Here's one IRV example with three strong candidates and where voters
do have some incentive to compromise.
45: A>B>C
10: B>A>C
15: B>C>A
30: C>B>A
We have one centrist candidate (B) between two others.
According to this poll it seems that B will be eliminated first, and
then A would win since some B supporters prefer A to C.
And where is this poll coming from? Even in an election that's polled
obsessively, with only two viable candidates, the poll results are all
over the map: http://www.pollster.com/blogs/pollster_accuracy_and_the_nati.php

We see popular-vote polling predicting Obama's margin as anything from
+2 to +11.

Vincent Conitzer and others have been doing some interesting work on
how easy/difficult it is to manipulate an election by changing votes.
An interesting corollary question is: how much information does a
manipulator need about the election profile in order to have a decent
chance of success?

One can imagine circumstances in which manipulation is easy (for Nader
supporters in Florida 2000, say), but, intuitive or not, how is a
voter going to have the kind of information (and confidence in it) to
successfully manipulate the above example. Not to mention the
recursive tangle we get into if we assume that *all* the voters share
this information...
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Juho Laatu
2008-11-22 19:50:18 UTC
Permalink
I assumed that the poll is just some regular
poll before the election. The final votes will
most probably be different, but probably not
too much different.

I agree that the results of polls may be all
over the map. That may be because of changes
in the opinions, changes in the way the questions
are presented, too small sample size etc. It
is also possible to publish strategic polls (with
biased/falsified information) with the intention
to influence the opinions, or the strategies that
others will use. And it is possible to refer to
those polls that one wants.

The fact that polls are inaccurate, conflicting,
and can not fully predict the opinions on the
election day has also an impact on the strategic
opportunities. Strategies that require detailed
knowledge of the opinions (and maybe also good
central control of the strategic voters) and that
may backfire are often too difficult to handle in
real life elections. Many Condorcet examples /
strategic opportunities fall in this category.
Also many IRV strategies may fall in this category.

For these reasons I like the idea of presenting the
strategic cases as example cases from real life
(not as theoretical extreme cases on paper, or only
as theoretical on/off criteria without considering
their negative impact and probability of success in
real life elections). Of course strategies will
also always be based on (inaccurate) polls, not e.g.
on exact knowledge on the ballots and ability to
change those ballots that one wants, and to keep
other ballots unchanged.

The inaccuracy of polls is thus often a positive
thing since it makes successful implementation of
strategies in may cases impractical.

Juho
Subject: polls and manipulation
Date: Saturday, 22 November, 2008, 8:01 PM
Post by Juho Laatu
Here's one IRV example with three strong
candidates and where voters do have some incentive to
compromise.
Post by Juho Laatu
45: A>B>C
10: B>A>C
15: B>C>A
30: C>B>A
We have one centrist candidate (B) between two others.
According to this poll it seems that B will be
eliminated first, and then A would win since some B
supporters prefer A to C.
And where is this poll coming from? Even in an election
that's polled obsessively, with only two viable
http://www.pollster.com/blogs/pollster_accuracy_and_the_nati.php
We see popular-vote polling predicting Obama's margin
as anything from +2 to +11.
Vincent Conitzer and others have been doing some
interesting work on how easy/difficult it is to manipulate
an election by changing votes. An interesting corollary
question is: how much information does a manipulator need
about the election profile in order to have a decent chance
of success?
One can imagine circumstances in which manipulation is easy
(for Nader supporters in Florida 2000, say), but, intuitive
or not, how is a voter going to have the kind of information
(and confidence in it) to successfully manipulate the above
example. Not to mention the recursive tangle we get into if
we assume that *all* the voters share this information...
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f***@pcc.edu
2008-11-22 22:51:02 UTC
Permalink
Kevin,

I know that you have studied Top Two Runoff more deeply than I have.

Here in Oregon measure 65 was defeated recently. It was a version of top two runoff in which the the first round of the runoff replaced the traditional primaries, i.e. it was cast as one grand open primary for all parties and all voters, from which the top two vote getters advance to the other stage in November.

It was interesting that the IRV organization FairVote was against the measure, even though there was no IRV initiative on the ballot.

It seems to me that Top Two Runoff might be more manipulable than the instant version of the same, since voters could vote insincerely in the first round without having to worry about that messing up their choice in the other stage.

I would be interested in your thoughts on this matter.

FWS
Post by Kevin Venzke
Actually some of us will argue that top-two runoff seems likely
to have
better Condorcet efficiency (in the abstract sense) than IRV. I
can see
an argument for both sides. But I would agree that they are
different
systems with different incentives.
Kristofer Munsterhjelm
2008-11-23 16:11:15 UTC
Permalink
Post by f***@pcc.edu
Kevin,
I know that you have studied Top Two Runoff more deeply than I have.
Here in Oregon measure 65 was defeated recently. It was a version of
top two runoff in which the the first round of the runoff replaced the
traditional primaries, i.e. it was cast as one grand open primary for
all parties and all voters, from which the top two vote getters advance
to the other stage in November.
It was interesting that the IRV organization FairVote was against the
measure, even though there was no IRV initiative on the ballot.
It seems to me that Top Two Runoff might be more manipulable than the
instant version of the same, since voters could vote insincerely in the
first round without having to worry about that messing up their choice
in the other stage.
I would be interested in your thoughts on this matter.
I'm not Kevin, but I think I can comment. In any method that's [some
base method] + runoff, where the runoff candidates are picked from the
social ordering of the base method, the existence of the second round
would increase the incentive to strategize.

However, it would not make it safe to always strategize. Say that the
runoff method is "pick first and second place winners of the base
method". Then any strategy that boosts your preferred candidate to
either first or second place can be used - but if the strategy, when
applied too greedily, causes both first and second place to be replaced
by candidates you don't like, there's an incentive to be careful.

That's weaker than it is for just applying the base method and picking
the winner. If you use strategy in the base method case, and you
displace your true winner in favor of someone that you really loathe,
then you're out of luck. For that to deter you from using strategy in a
runoff, it has to displace both the candidates that would get into the
runoffs.

One should also be aware that the second round, taken as a separate
election, will be honest. That's because there are only two candidates
and a simple majority election is strategyproof in that case. So that
may weight against the increased incentive to use strategy in the first
round. Whether this makes the method (in general) more fragile
(attracting more strategy) or more robust depends on which component is
stronger: the incentive to strategy in the first round, or to honesty in
the second. That probably depends on the base method.

There may also be inter-round strategy. Say that there are two wings and
a center. In the first round, the left wing runs a strategy. It's
discovered. Now, the centrists may support the right-wing candidate in
the second round "just to show them", whereas they wouldn't otherwise.
To the degree that runoffs are two elections, such effects may occur.
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James Gilmour
2008-11-23 18:04:09 UTC
Permalink
Kristofer Munsterhjelm > Sent: Sunday, November 23, 2008 4:11 PM
Post by Kristofer Munsterhjelm
I'm not Kevin, but I think I can comment. In any method that's [some
base method] + runoff, where the runoff candidates are picked from the
social ordering of the base method, the existence of the second round
would increase the incentive to strategize.
So what happened to the incentive to strategize in the first round of the 2002 French Presidential election?

First Round Results
Jacques Chirac Rally for France (RPF) 19.83%
Jean-Marie Le Pen National Front (FN) 16.91%
Lionel Jospin Socialist Party (PS) 16.14%
François Bayrou Union for French Democracy (UDF) 6.84%
Arlette Laguiller Workers' Struggle (LO) 5.73%
Jean-Pierre Chevènement Citizens' Movement (MC) 5.33%
Noël Mamère Greens (Vert) 5.24%
Olivier Besancenot Revolutionary Communist League (LCR) 4.26%
Jean Saint-Josse Hunting, Fishing, Nature and Traditions (CPNT) 4.25%
Alain Madelin Liberal Democracy (DL) 3.92%
Robert Hue Communist Party (PCF) 3.38%
Bruno Mégret National Republican Movement (MNR) 2.35%
Christiane Taubira Radical Left Party 2.32%
Corinne Lepage Citizenship, Action, Participation Movement (MCAP) 1.88%
Christine Boutin Social Republican Forum (FRS) 1.19%
Daniel Gluckstein Workers' Party (PT) 0.47%
ELECTORATE: 40,320,334
TURNOUT: 29,149,143

The second round of this TTRO election was a choice between one candidate from the centre-right and one candidate from the extreme
right, despite two-thirds of the voters supporting candidates from the left.
Jacques Chirac received 25,316,647 votes (82.14%) and Jean-Marie Le Pen received 5,502,314 (17.85%). Around 4% of votes were spoilt
in protest and 20% of the electorate did not vote.

I am convinced that had this been an exhaustive ballot (multi-round run-off), IRV or Condorcet election, the result would have been
quite different. Certainly the final "top two" choice would have been very different.

The effects of TTRO are well known, but this is what real political parties do in real TTRO elections (in terms of nominating
candidates), and is what real voters do in real TTRO elections (in terms of scattering their votes around), and the results are
disastrous - and not just for the French in this case - we all had to live with the political consequences of this election.

James Gilmour

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Kristofer Munsterhjelm
2008-11-23 19:38:14 UTC
Permalink
Post by James Gilmour
Kristofer Munsterhjelm > Sent: Sunday, November 23, 2008 4:11 PM
Post by Kristofer Munsterhjelm
I'm not Kevin, but I think I can comment. In any method that's [some
base method] + runoff, where the runoff candidates are picked from the
social ordering of the base method, the existence of the second round
would increase the incentive to strategize.
So what happened to the incentive to strategize in the first round of
the 2002 French Presidential election?
First Round Results
Jacques Chirac Rally for France (RPF) 19.83%
Jean-Marie Le Pen National Front (FN) 16.91%
Lionel Jospin Socialist Party (PS) 16.14%
François Bayrou Union for French Democracy (UDF) 6.84%
Arlette Laguiller Workers' Struggle (LO) 5.73%
Jean-Pierre Chevènement Citizens' Movement (MC) 5.33%
Noël Mamère Greens (Vert) 5.24%
Olivier Besancenot Revolutionary Communist League (LCR) 4.26%
Jean Saint-Josse Hunting, Fishing, Nature and Traditions (CPNT) 4.25%
Alain Madelin Liberal Democracy (DL) 3.92%
Robert Hue Communist Party (PCF) 3.38%
Bruno Mégret National Republican Movement (MNR) 2.35%
Christiane Taubira Radical Left Party 2.32%
Corinne Lepage Citizenship, Action, Participation Movement (MCAP) 1.88%
Christine Boutin Social Republican Forum (FRS) 1.19%
Daniel Gluckstein Workers' Party (PT) 0.47%
ELECTORATE: 40,320,334
TURNOUT: 29,149,143
There was no strategizing (that I can see), and the left-leaning parties
split the vote. TTR isn't perfect, I never claimed that.

When I wrote my reply, I was referring to the kind of strategy that
could backfire on the voters if it's taken too far - something like
burial in Condorcet. That is the sort of strategy you wouldn't want, and
I said that I thought runoff systems would have more of them in the
first round because the stakes would be lower. On the other hand, the
second round, or last if there are more than two, must be (and is) honest.

I am a bit surprised that nobody were doing any sort of pushover
strategy here, but then, they might; there's too little information to
say and I don't know the general French opinion at the time.
Post by James Gilmour
The second round of this TTRO election was a choice between one
candidate from the centre-right and one candidate from the extreme
right, despite two-thirds of the voters supporting candidates from
the left.
Jacques Chirac received 25,316,647 votes (82.14%) and Jean-Marie Le
Pen received 5,502,314 (17.85%). Around 4% of votes were spoilt
in protest and 20% of the electorate did not vote.
I am convinced that had this been an exhaustive ballot (multi-round
run-off), IRV or Condorcet election, the result would have been
quite different. Certainly the final "top two" choice would have been
very different.
Plurality is a really bad method. TTR is better, but TTR is ultimately
based on Plurality. Condorcet + top two, or Approval + top two, or
something like that, would have provided better results as well, I
think; the question is whether it'd be sufficiently better than the
method without top two that it'd be worth it.

If you're referring to how I've earlier supported TTR above IRV, well,
in this case, IRV might have given the right result. But then again, the
dynamics could have been different. Would there have been that many
parties had all previous elections been IRV and not TTR?
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Dave Ketchum
2008-11-24 02:11:01 UTC
Permalink
Post by James Gilmour
Kristofer Munsterhjelm > Sent: Sunday, November 23, 2008 4:11 PM
Post by Kristofer Munsterhjelm
I'm not Kevin, but I think I can comment. In any method that's [some
base method] + runoff, where the runoff candidates are picked from the
social ordering of the base method, the existence of the second round
would increase the incentive to strategize.
With 2/3 of the voters agreed they will vote left, they could have made out
much better with Condorcet. Even if all voted the indicated first choice
it would not have taken many second choice Jospin votes for him to win.
Some others also were possibilities with Condorcet.

Debatable whether a runoff would have been appropriate with Condorcet.
Unlike Plurality, it permits voters to more completely express their desires.

DWK
Post by James Gilmour
So what happened to the incentive to strategize in the first round of the 2002 French Presidential election?
First Round Results
Jacques Chirac Rally for France (RPF) 19.83%
Jean-Marie Le Pen National Front (FN) 16.91%
Lionel Jospin Socialist Party (PS) 16.14%
François Bayrou Union for French Democracy (UDF) 6.84%
Arlette Laguiller Workers' Struggle (LO) 5.73%
Jean-Pierre Chevènement Citizens' Movement (MC) 5.33%
Noël Mamère Greens (Vert) 5.24%
Olivier Besancenot Revolutionary Communist League (LCR) 4.26%
Jean Saint-Josse Hunting, Fishing, Nature and Traditions (CPNT) 4.25%
Alain Madelin Liberal Democracy (DL) 3.92%
Robert Hue Communist Party (PCF) 3.38%
Bruno Mégret National Republican Movement (MNR) 2.35%
Christiane Taubira Radical Left Party 2.32%
Corinne Lepage Citizenship, Action, Participation Movement (MCAP) 1.88%
Christine Boutin Social Republican Forum (FRS) 1.19%
Daniel Gluckstein Workers' Party (PT) 0.47%
ELECTORATE: 40,320,334
TURNOUT: 29,149,143
The second round of this TTRO election was a choice between one candidate from the centre-right and one candidate from the extreme
right, despite two-thirds of the voters supporting candidates from the left.
Jacques Chirac received 25,316,647 votes (82.14%) and Jean-Marie Le Pen received 5,502,314 (17.85%). Around 4% of votes were spoilt
in protest and 20% of the electorate did not vote.
I am convinced that had this been an exhaustive ballot (multi-round run-off), IRV or Condorcet election, the result would have been
quite different. Certainly the final "top two" choice would have been very different.
The effects of TTRO are well known, but this is what real political parties do in real TTRO elections (in terms of nominating
candidates), and is what real voters do in real TTRO elections (in terms of scattering their votes around), and the results are
disastrous - and not just for the French in this case - we all had to live with the political consequences of this election.
James Gilmour
--
***@clarityconnect.com people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.



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Juho Laatu
2008-11-23 19:25:30 UTC
Permalink
Say that the runoff method is "pick first and second
place winners of the base method". Then any strategy
that boosts your preferred candidate to either first or
second place can be used
One could also promote a candidate that is likely to
lose to one's favourite at the second round. Here's one
example.

(To fsimmons) In this example TTR is also less Condorcet
efficient (in addition to being more manipulable).

Sincere opinions:
45: A>B>C
15: B>A>C
15: B>C>A
25: C>B>A

In both TTR and IRV (with sincere voting) the second
round would be between A and B. B would win.

If 10 of the 45 A supporters would vote for C at the
first round in TTR, then the second round would be
between A and C, and A would win. But in IRV the
strategic A supporters would be bound to vote for C
at the second round, and C would win.

(If too many A voters vote for C at the first round,
then the second round will be between B and C. But
this is still safe to from the A supporters' point
of view (if the polls are accurate) since also
without the strategy B would win.)
"just to show them"
Yes, the reactions of people to strategies are
important. One should check also these factors
systematically when estimating the feasibility
of different strategies in real life.

There may be societies where those that do not
use strategies are considered fools, but there
are also societies where trying to cheat to win
is seen as a very bad thing.

Strategic attempts may backfire already at the
first round. In large public elections strategies
that require coordination or marketing can not be
hidden.


Some further (rather wild) speculation:
- One could arrange elections with as many rounds
as needed (maybe without elimination)
- Maybe this is more valid for electorates or
permanent bodies like parliamnets than for large
public elections (unless electrical and PC/mobile
based)
- One approach is to change the candidate proposals
as needed after each round to help reaching consensus
- One could e.g. elect both the prime minister,
government coalition and political program at the
same time (each proposal would consist of a
combination of such components)
- One could use Condorcet and vote until a Codorcet
winner is found
- Parties and politicians would modify their
proposals until a good enough proposal is found
- Maybe there would be some special rule to
termoinate the process if it gets too long
- One possibility would be to start reducing the >50%
limit (to win all other proposals) after say 10 rounds

Juho
Subject: Re: [EM] Top Two Runoff versus Instant Top To Runoff
Date: Sunday, 23 November, 2008, 6:11 PM
Post by f***@pcc.edu
Kevin,
I know that you have studied Top Two Runoff more
deeply than I have. Here in Oregon measure 65 was defeated
recently. It was a version of top two runoff in which the
the first round of the runoff replaced the traditional
primaries, i.e. it was cast as one grand open primary for
all parties and all voters, from which the top two vote
getters advance to the other stage in November.
Post by f***@pcc.edu
It was interesting that the IRV organization FairVote
was against the measure, even though there was no IRV
initiative on the ballot.
Post by f***@pcc.edu
It seems to me that Top Two Runoff might be more
manipulable than the instant version of the same, since
voters could vote insincerely in the first round without
having to worry about that messing up their choice in the
other stage.
Post by f***@pcc.edu
I would be interested in your thoughts on this
matter.
I'm not Kevin, but I think I can comment. In any method
that's [some base method] + runoff, where the runoff
candidates are picked from the social ordering of the base
method, the existence of the second round would increase the
incentive to strategize.
However, it would not make it safe to always strategize.
Say that the runoff method is "pick first and second
place winners of the base method". Then any strategy
that boosts your preferred candidate to either first or
second place can be used - but if the strategy, when applied
too greedily, causes both first and second place to be
replaced by candidates you don't like, there's an
incentive to be careful.
That's weaker than it is for just applying the base
method and picking the winner. If you use strategy in the
base method case, and you displace your true winner in favor
of someone that you really loathe, then you're out of
luck. For that to deter you from using strategy in a runoff,
it has to displace both the candidates that would get into
the runoffs.
One should also be aware that the second round, taken as a
separate election, will be honest. That's because there
are only two candidates and a simple majority election is
strategyproof in that case. So that may weight against the
increased incentive to use strategy in the first round.
Whether this makes the method (in general) more fragile
(attracting more strategy) or more robust depends on which
component is stronger: the incentive to strategy in the
first round, or to honesty in the second. That probably
depends on the base method.
There may also be inter-round strategy. Say that there are
two wings and a center. In the first round, the left wing
runs a strategy. It's discovered. Now, the centrists may
support the right-wing candidate in the second round
"just to show them", whereas they wouldn't
otherwise. To the degree that runoffs are two elections,
such effects may occur.
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Bob Richard
2008-11-23 20:07:19 UTC
Permalink
Post by f***@pcc.edu
It was interesting that the IRV organization FairVote
was against the measure, even though there was no IRV
initiative on the ballot.
I can't speak for FairVote, but I can state my own reasons for being
against Measure 65 in Oregon, as well as the already-implemented
Initiative 872 in the State of Washington and a very similar proposal
being supported by Governor Schwarzenegger in California.

First, while there was no IRV proposal on the ballot along side Measure
65, there is an active IRV movement in Oregon. It is currently focused
mainly on local government as opposed to state government and Congress.
This is consistent with electoral reform strategy in most other places
in the U.S. Also, ranked choice voting methods are explicitly provided
for in the state constitution, although there is no enabling legislation,.

Second, and equally important for me, two-round runoff/top-two proposals
differ greatly in their treatment of political parties. It's possible to
structure them so parties nominate by convention, caucuses or privately
run primary. In these cases, each party controls the use of its name by
the candidates. But it's also possible to structure top-two so the role
of parties is reduced to various extents.

The top-two system now in effect in Washington gives individual
candidates the opportunity to call themselves anything they want on the
ballot (one Republican candidate chose "GOP" as his party label). The
parties have no say in this. As another example, California Proposition
62, which was rejected by the voters in 2004, would have allowed each
party to determine for each election whether candidates registered with
that party would be identified as such on the ballot and in government
publications. Parties would have to have made that decision for the
election as a whole, not on a candidate-by-candidate basis. The current
California proposal is very similar to Washington. I believe (but
haven't looked this up), that the proposal voted down in Oregon this
month, by about 65-35, was also modeled on Washington.

The motivation for all of these proposals have more to do with limiting
the role of political parties than it does with insuring majority
support for the winner.

Top-two is better than plurality (and potentially a step toward IRV
later on) but *only* if it doesn't infringe on the right of parties to
nominate candidates. I am against Washington's flavor of top-two and was
against Oregon Measure 65. But if someone puts a top-two proposal on the
ballot that allows each political party to determine which candidate or
candidates can use its name, I'd vote for it unless IRV was already on
the table (as is at least arguably the case in Oregon).

--Bob Richard
Post by f***@pcc.edu
Kevin,
I know that you have studied Top Two Runoff more deeply than I have.
Here in Oregon measure 65 was defeated recently. It was a version of
top two runoff in which the the first round of the runoff replaced the
traditional primaries, i.e. it was cast as one grand open primary for
all parties and all voters, from which the top two vote getters
advance to the other stage in November.
It was interesting that the IRV organization FairVote was against the
measure, even though there was no IRV initiative on the ballot.
It seems to me that Top Two Runoff might be more manipulable than the
instant version of the same, since voters could vote insincerely in
the first round without having to worry about that messing up their
choice in the other stage.
I would be interested in your thoughts on this matter.
FWS
Post by Kevin Venzke
Actually some of us will argue that top-two runoff seems likely
to have
better Condorcet efficiency (in the abstract sense) than IRV. I
can see
an argument for both sides. But I would agree that they are
different
systems with different incentives.
------------------------------------------------------------------------
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--
Bob Richard
Marin Ranked Voting
P.O. Box 235
Kentfield, CA 94914-0235
415-256-9393
http://www.marinrankedvoting.org
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Kevin Venzke
2008-11-23 20:39:55 UTC
Permalink
Hi Forest,
Post by f***@pcc.edu
It seems to me that Top Two Runoff might be more
manipulable than the instant version of the same, since
voters could vote insincerely in the first round without
having to worry about that messing up their choice in the
other stage.
I would be interested in your thoughts on this matter.
Not sure I follow. I guess you mean that Chirac voters could instead vote
for Le Pen, forcing voters on the Left to support Chirac in the second
round when under IRV they would not have seen any need to support Chirac
over Le Pen.

That's possible, but I think it's far more likely that this mechanic works
in a positive way. Under IRV the possibility that a too-obscure candidate
(or a candidate in the same vein as a frontrunner but without official
backing) won't receive any lower rankings would be a serious obstacle.
Under TTR his supporters can try to place him in the top two with much
less risk, since if he makes the top two and really is preferable to the
other top-two candidate, other voters can provide their support later, in
the second round.

I think both the good and the bad of TTR come from reduced nomination
disincentive and with this the ability to vote more *sincerely* (in a
sense: If they were "insincere" otherwise it may be because the candidate
did not run).


I think the following preserves most of the good and gets rid of most of
the bad.

How does FPP stay limited to two viable candidates? You lose nothing by
voting for 2nd place, and a vote for 3rd place is really a vote for 1st
place.

So change TTR to make it so that you lose nothing by voting for 3rd place
(what it already has), and a vote for *fourth* place is really a vote for
1st place.

In other words: The first-round winner is automatically elected as long
as he has more votes than second and third place combined. He doesn't have
to beat candidates who do worse than that.

More consolidation (i.e. to get down to three candidates) before the
first round should, I think, make it more likely that the second round
isn't always between the same players.

This fails if it can't be expected that one candidate could get enough
votes to beat the next two. But how likely is that? How often is FPP that
fragmented? All it would take is for one candidate to develop some
momentum, and it would become too risky to not consolidate.

We also still have FPP's spoiler problem, though not as bad.

I also like to consider using this first round as a filter to get us to
a second round that uses a completely different election method (esp.
one that isn't defined for more than three candidates, or is too
manipulable if nominations can be made directly).

Kevin Venzke




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Kristofer Munsterhjelm
2008-11-23 19:21:53 UTC
Permalink
Post by Greg
I have written up my reasons for preferring IRV over Condorcet methods
http://www.gregdennis.com/voting/irv_vs_condorcet.html
I welcome any comments you have.
I'll try to do so, then. Note that I support Condorcet.

Regarding reason number one, it is true that if there are minor parties
that make no difference, IRV will act as if they didn't exist. That is;
as long as they get a smaller share of the votes than any of those who
would matter, they are excluded. However, as soon as a former minor
third party grows large enough, it destabilizes IRV. You can see this in
the Yee diagrams for IRV, where the borders near candidates become
noisy (and this noise some times travels well into the regions of the
candidates themselves). This may be what you're conceding regarding
center squeeze, but the problem is not only the third party's, it's all
the participants', since the destabilization turns IRV a lot more random
(because of the amplifying nature of the elimination).

IRV may elect Condorcet winners, but if you accept that electing
Condorcet winners is a good thing, then simple tweaks will make IRV even
better: one may check for a Condorcet winner (among the remaining
candidates) after each elimination, or eliminate the one of the two
bottom rated that loses the pairwise contest between the two. Also, the
picture may be false: if we were to count Plurality elections as
Condorcet elections, one of the two major parties would undoubtedly be
the Condorcet winner according to the ballots, but this is merely
because of strategy.

Regarding number two, simple Condorcet methods exist. Borda-elimination
(Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody
who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll
partially grant this, though, since the good methods are complex, but
I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In
MAM, you take all the pairwise contests, sort by strength, and affirm
down the list unless you would contradict an earlier affirmed contest.
This method is cloneproof, monotonic, etc...

Perhaps you could explain it in that "say A won. B's supporters are
going to say "but some people preferred B to A!". Then you can say, but
more people preferred C to B and A to C". I'm not sure, there may be
better explanations.

Even if so, this does provide a hard choice, though. I'll grant that,
since as far as Condorcet methods have momentum as election methods,
Schulze has the most. I wonder if there are simpler heuristics for
Schulze than beatpaths. Schulze's mentioned the Schwartz set heuristic
(which I think would be hard to explain) and the arborescence heuristic
(which I don't know what is).

There's also the observation that voters may not need to know the
method. Some counties in New Zealand use Meek STV, which basically uses
a convergence algorithm to determine the weights of the ballots after a
candidate is elected. That's quite complex, yet they still use it.

Regarding the third and fourth, I'll again say that some Condorcet
methods are more resistant to burial than others. The IRV modifications
I talked about earlier resists burial - Chris Benham showed that the
"check for a Condorcet winner" modification passes "mutual dominant
third burial resistance", meaning that you can't bury a candidate that
would be in the honest mutual dominant third set. Unfortunately, the
modification is also nonmonotonic (like IRV is). While I'll have to
grant this, I'll say that pushover isn't that unintuitive. Imagine a
runoff; now stack the deck against your opponent by making the method
elect those who would split your opponent's vote. The randomness or
chaos of IRV, as mentioned in the first point response, may make this
more difficult than one would expect, but to the extent that is true,
IRV suffers from the chaos itself.

Also, you use examples to show that by demanding core support, IRV gets
rid of unknowns. However, IRV can fail to elect candidates with
significant core support. Warren has an example of that at
http://rangevoting.org/CoreSupp.html .

Regarding number five, I would think that IRV would limit Condorcet
rather than making it feasible. Consider the case where IRV is passed
but nothing significant happens to the distribution of power. Then we
say "Hey, IRV is bad, but give us a chance, try Condorcet". The voters
may readily say "you got your chance, and election methods don't seem to
matter anyway, we just get two party rule". In addition, if IRV doesn't
do anything, we're still left with a two party regime, and those parties
will be very interested in blocking Condorcet. To the extent applicable,
the Australian House of Representatives election may show whether IRV
supports multiple parties: in this case, it doesn't seem to do so (the
House usually being populated by three parties, but the National and
Liberal parties are usually grouped together as they stay in the same
coalition). I add he qualifier "to the extent applicable" because one
could argue that other features of the Australian system, such as
compulsory full ranking and how-to-vote cards, is the cause of this.

The Australian example can also be used against number six -- if it is
IRV that's the problem. If IRV supports few parties, it won't really
help in trying to change a two-party system into a multiparty one. In
the best case, we have Ireland, where the president has little effective
power, so that the STV component (which is much better than per-district
IRV, in my opinion) prevails. In worse cases, we have the Australian
outcome, with multiple parties in one body (the Senate) but not in the
other (the House). In the worst case, there would be no STV component at
all.

I'll grant the point about Condorcet multiwinner elections. This, in my
opinion, means that we should try to find a good (polytime) multiwinner
election method that reduces to Condorcet. CPO-STV is too complex, and
Schulze STV needs a lot of space (to my knowledge). I'll also note that
it's possible to make multiwinner versions of other non-Condorcet
methods; I did so with Bucklin, for instance.

The seventh point is good if you agree with the fifth, but not if you
don't. I don't, so I think this could be a problem. At least we'll get
STV if your sixth point is true, but even that may not be. As for the
unintuitive nature of Condorcet, Ranked Pairs seems pretty intuitive to
me (with the "complaints rebuffed by stronger complaints" nature); even
if not, everybody knows about tournaments and Copeland, and even if not,
I think IRV should be strengthened by the simple modifications if
Condorcet compliance is important (as you have said it is).

-

This reply has not considered the direct advantages of most Condorcet
methods, like being countable in districts (when using matrices at
least) or being monotonic. Those should also be acknowledged; Condorcet
has some weaknesses (like burial problems, except a few methods), but
IRV has others, and I think they are more serious.
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Juho Laatu
2008-11-23 20:47:21 UTC
Permalink
Post by Kristofer Munsterhjelm
Regarding number two, simple Condorcet methods exist.
Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax
is quite simple, and everybody who's dealt with sports
knows Copeland (with Minmax tiebreaks). I'll partially
grant this, though, since the good methods are complex
Minmax is both simple and good. I think at least minmax(margins) is a good solution for many needs.

The weakest spot of minmax(margins) could be that it fails mutual majority. That means for example that nominating a set of clones instead of just one candidate could lead (at least in theory) to not winning the election.

On the other hand other methods than minmax(margins) may not respect the good idea of mmm to elect the candidate that has the least incentive among voters to be changed to some other of the candidates.

(Minmax(margins) fails also Smith and Condorcet loser, but those violations can be explained to be intentional and positive.)
Post by Kristofer Munsterhjelm
, but
I'll ask whether you think MAM (Ranked Pairs(wv)) is too
complex. In MAM, you take all the pairwise contests, sort by
strength, and affirm down the list unless you would
contradict an earlier affirmed contest. This method is
cloneproof, monotonic, etc...
Perhaps you could explain it in that "say A won.
B's supporters are going to say "but some people
preferred B to A!". Then you can say, but more people
preferred C to B and A to C". I'm not sure, there
may be better explanations.
Also minmax(margins) is close to this. It has a very natural explanation. (I gave one rough explanation above. Another one is "elect the candidate that needs least additional votes to win all others".)


I don't claim that Minmax(margins) would be the best Condorcet method for all needs. I rather claim that there are many kind of elections and there are many alternative targets. Minmax (margins) emphasizes small opposition (in favour of any other single candidate) against the elected candidate.

This justification focuses on the performance with sincere votes. Also other good criteria that describe which candidate would be the best may be used..

Another direction is to look for a method that is most resistent to straegic voting. (Many of the best known criteria emphasize this viewpoint.)

If the environment where the method will be used in plagued with widespread strategic voting then it makes sense to emphasize the "strategy free" oriented criteria a bit. If the voters are expected to be predominantly sincere then one has the luxury to focus on criteria that aim at electing the best winner.

There are thus different kind of environments and different kind of needs. One should pick the best method for each need and environment. Somewhere it may be e.g. FPTP or minmax(margins), somewhere something else.

Juho







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Kristofer Munsterhjelm
2008-11-25 11:37:49 UTC
Permalink
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Regarding number two, simple Condorcet methods exist.
Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax is quite
simple, and everybody who's dealt with sports knows Copeland (with
Minmax tiebreaks). I'll partially grant this, though, since the
good methods are complex
Minmax is both simple and good. I think at least minmax(margins) is a
good solution for many needs.
The weakest spot of minmax(margins) could be that it fails mutual
majority. That means for example that nominating a set of clones
instead of just one candidate could lead (at least in theory) to not
winning the election.
On the other hand other methods than minmax(margins) may not respect
the good idea of mmm to elect the candidate that has the least
incentive among voters to be changed to some other of the candidates.
I think Schulze said that his method was the one that agreed most with
Minmax while still being cloneproof. According to Warren, that is true
(he refers to simulations made by Petry and Heitzig) - see
http://rangevoting.org/SchulzeExplan.html .

At the other end of "generalizable methods" you have Kemeny. Kemeny is
not cloneproof (it suffers from crowding). I wonder what "Cloneproof
Kemeny" would look like, but there have been attempts to move Ranked
Pairs closer to Kemeny. See Heitzig's Short Ranked Pairs:
http://listas.apesol.org/pipermail/election-methods-electorama.com/2004-November/014208.html
Post by Juho Laatu
(Minmax(margins) fails also Smith and Condorcet loser, but those
violations can be explained to be intentional and positive.)
That's a problem, in my opinion. A voting method also is a metric of who
deserves to win. In that point of view, if the metric says that
Condorcet winners are good, but the method can elect Conorcet losers,
the metric is self-contradictory. As for Smith, I would like to have
that as well, since if the method says Condorcet for a candidate, it
should also say Condorcet for a set (unless there's some overriding
strategy-proofing reason as to why not).
Post by Juho Laatu
Post by Kristofer Munsterhjelm
, but I'll ask whether you think MAM (Ranked Pairs(wv)) is too
complex. In MAM, you take all the pairwise contests, sort by
strength, and affirm down the list unless you would contradict an
earlier affirmed contest. This method is cloneproof, monotonic,
etc...
Perhaps you could explain it in that "say A won. B's supporters are
going to say "but some people preferred B to A!". Then you can say,
but more people preferred C to B and A to C". I'm not sure, there
may be better explanations.
Also minmax(margins) is close to this. It has a very natural
explanation. (I gave one rough explanation above. Another one is
"elect the candidate that needs least additional votes to win all
others".)
Kemeny is also quite simple, I suppose. It's merely "Find the ordering
where most people agree with the preferences". However, it's not in
polytime; finding the winner, asymptotically, is very hard (though
linear programming tricks can be used, that makes the method extremely
complex). I don't think Kemeny is Smith, either.
Post by Juho Laatu
I don't claim that Minmax(margins) would be the best Condorcet method
for all needs. I rather claim that there are many kind of elections
and there are many alternative targets. Minmax (margins) emphasizes
small opposition (in favour of any other single candidate) against
the elected candidate.
This justification focuses on the performance with sincere votes.
Also other good criteria that describe which candidate would be the
best may be used..
Another direction is to look for a method that is most resistent to
straegic voting. (Many of the best known criteria emphasize this
viewpoint.)
If the environment where the method will be used in plagued with
widespread strategic voting then it makes sense to emphasize the
"strategy free" oriented criteria a bit. If the voters are expected
to be predominantly sincere then one has the luxury to focus on
criteria that aim at electing the best winner.
The problem is that we don't know how strategic people, or parties are
going to be. This depends on the nation and people; when New York
briefly had STV, the parties almost immediately turned to vote
management, but other countries with STV have been free of vote
management. I think Ireland is one of the latter.

One way to deal with this is to make the method maximally safe against
strategy. However, for some types of strategy this makes the method
return worse results were the voters honest. Say there's an election
where the "unaugmented winner" is X. If the method is strategy-hardened,
the winner will be Y instead. Then there may be an instance in which
people truly wanted X, but also another instance where the people truly
wanted Y but some employed strategy. The method can't read people's
minds and thus can't know which is the case, which means that any case
of the former would lead to a worse result if the method was
strategy-hardened.

Benham's Dominant Mutual Quarter Burial Resistance example comes to mind:

26: A>B
25: C>A
49: B>C (sincere is B>A or B)

If these ballots were sincere, one would expect B to win (and almost all
methods elect B). However, if it's true that the 49 voters are on a
burial spree, then it would be a bad thing to elect B. But the method
can't tell which is the case from the ballots alone.

In that sense, some strategy hardening is more expensive than others. If
the hardening only involves ballot situations that would very rarely
appear honestly, or if the candidate it elects to deter strategy is only
slightly worse than that it would otherwise elect, then the hardening is
"cheap". Otherwise, it's expensive. Some strategy hardening is next to
free, I think; cases where the strategy applies *because* the method is
bad at picking honest winners, not because it's good.
Post by Juho Laatu
There are thus different kind of environments and different kind of
needs. One should pick the best method for each need and environment.
Somewhere it may be e.g. FPTP or minmax(margins), somewhere something
else.
Given the above, that's right. I can't quite see the situation where
FPTP would be preferred, except possibly where there are only ever two
choices (but most methods reduce to FPTP in that case).

Even though I've said it before, I'll repeat my runoff idea: to have two
different methods, one very resistant to strategy, and another good at
finding honest winners, and picking the winners from each for the
runoff. It would be extremely complex, though (I remember one reply
saying to the effect of "You can't be serious!"). It could also,
perhaps, tempt the population to vote more strategically since "less is
on the line", as I talked about in my message about TTR.
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Juho Laatu
2008-11-25 19:09:05 UTC
Permalink
--- On Tue, 25/11/08, Kristofer Munsterhjelm <km-***@broadpark.no> wrote:

I'll try to answer very shortly to most of the points.
I can comment more if there are some interesting ones.
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Tuesday, 25 November, 2008, 1:37 PM
--- On Sun, 23/11/08, Kristofer Munsterhjelm
Post by Kristofer Munsterhjelm
Regarding number two, simple Condorcet methods
exist. Borda-elimination (Nanson or Raynaud) is Condorcet.
Minmax is quite
Post by Kristofer Munsterhjelm
simple, and everybody who's dealt with sports
knows Copeland (with
Post by Kristofer Munsterhjelm
Minmax tiebreaks). I'll partially grant this,
though, since the
Post by Kristofer Munsterhjelm
good methods are complex
Minmax is both simple and good. I think at least
minmax(margins) is a
good solution for many needs.
The weakest spot of minmax(margins) could be that it
fails mutual
majority. That means for example that nominating a set
of clones
instead of just one candidate could lead (at least in
theory) to not
winning the election.
On the other hand other methods than minmax(margins)
may not respect
the good idea of mmm to elect the candidate that has
the least
incentive among voters to be changed to some other of
the candidates.
I think Schulze said that his method was the one that
agreed most with Minmax while still being cloneproof.
According to Warren, that is true (he refers to simulations
made by Petry and Heitzig) - see
http://rangevoting.org/SchulzeExplan.html .
The claim seems to be about Smith//MinMax.
At the other end of "generalizable methods" you
have Kemeny. Kemeny is not cloneproof (it suffers from
crowding). I wonder what "Cloneproof Kemeny" would
look like, but there have been attempts to move Ranked Pairs
http://listas.apesol.org/pipermail/election-methods-electorama.com/2004-November/014208.html
Note that the minmax philosophy is to study paths of
length one. Minmax philosophy says that voter interest
to replace the elected candidate with another is more
relevant than their interest to replace the candidates
in chain. (Such chains of changes do not typically
happen in real life after the election.)
(Minmax(margins) fails also Smith and Condorcet loser,
but those
violations can be explained to be intentional and
positive.)
That's a problem, in my opinion. A voting method also
is a metric of who deserves to win.
Yes if one sets that as a target. The alternative is
to emphasize also other aspects like being free of
strategic voting related risks. I think minmax can be
seen as an ideal definition (for some needs) of which
candidate is best.
In that point of view,
if the metric says that Condorcet winners are good, but the
method can elect Conorcet losers, the metric is
self-contradictory.
Minmax may elect the Condorcet loser only when there
is no Condorcet winner. And only in situations where
all other candidates are worse than the Condorcet
loser from the minmax philosophy/utility point of view.
As for Smith, I would like to have that
as well, since if the method says Condorcet for a candidate,
it should also say Condorcet for a set (unless there's
some overriding strategy-proofing reason as to why not).
I don't see that as a requirement even if there were
no strategy-proofing needs. The minmax philosophy says
that voters may have more interest to replace the
elected Smith set member with another member of the
set than they have interest to replace someone outside
of that set with others.
Post by Kristofer Munsterhjelm
, but I'll ask whether you think MAM (Ranked
Pairs(wv)) is too complex. In MAM, you take all the pairwise
contests, sort by strength, and affirm down the list unless
you would contradict an
Post by Kristofer Munsterhjelm
earlier affirmed contest. This method is
cloneproof, monotonic,
Post by Kristofer Munsterhjelm
etc...
Perhaps you could explain it in that "say A
won. B's supporters are
Post by Kristofer Munsterhjelm
going to say "but some people preferred B to
A!". Then you can say,
Post by Kristofer Munsterhjelm
but more people preferred C to B and A to C".
I'm not sure, there may be better explanations.
Also minmax(margins) is close to this. It has a very
natural
explanation. (I gave one rough explanation above.
Another one is
"elect the candidate that needs least additional
votes to win all
others".)
Kemeny is also quite simple, I suppose. It's merely
"Find the ordering where most people agree with the
preferences".
One could see Kemeny as a good definition of a good
social ordering. That may or may not correlate with
the definition of the best single winner.
However, it's not in polytime;
finding the winner, asymptotically, is very hard (though
linear programming tricks can be used, that makes the method
extremely complex). I don't think Kemeny is Smith,
either.
I don't claim that Minmax(margins) would be the
best Condorcet method
for all needs. I rather claim that there are many kind
of elections
and there are many alternative targets. Minmax
(margins) emphasizes
small opposition (in favour of any other single
candidate) against
the elected candidate.
This justification focuses on the performance with
sincere votes.
Also other good criteria that describe which candidate
would be the
best may be used..
Another direction is to look for a method that is most
resistent to
straegic voting. (Many of the best known criteria
emphasize this
viewpoint.)
If the environment where the method will be used in
plagued with
widespread strategic voting then it makes sense to
emphasize the
"strategy free" oriented criteria a bit. If
the voters are expected
to be predominantly sincere then one has the luxury to
focus on
criteria that aim at electing the best winner.
The problem is that we don't know how strategic people,
or parties are going to be. This depends on the nation and
people; when New York briefly had STV, the parties almost
immediately turned to vote management, but other countries
with STV have been free of vote management. I think Ireland
is one of the latter.
Yes. One has to guess, or one may modify the system when
one sees the level of strategic voting and its level of
impact. In general I believe strategic voting would not
be as bad as discussions on this list might suggest.
Take for example all the numerous Top Two Runoff
elections today. People speculate on strategic
possibilities and other problems only afterwards but
in most cases they vote sincerely in the elections.
One way to deal with this is to make the method maximally
safe against strategy. However, for some types of strategy
this makes the method return worse results were the voters
honest. Say there's an election where the
"unaugmented winner" is X. If the method is
strategy-hardened, the winner will be Y instead. Then there
may be an instance in which people truly wanted X, but also
another instance where the people truly wanted Y but some
employed strategy. The method can't read people's
minds and thus can't know which is the case, which means
that any case of the former would lead to a worse result if
the method was strategy-hardened.
Yes, there is always a trade-off. Maybe it is a worse
failure to elect a wrong winner due to a successful
strategic plot than due to a method that doesn't
always elect the best winner. But failure to elect
the best possible winner with sincere votes is a
serious problem too.

One observation about clones. One can get the same
pairwise matrix from ballots that contain clones and
from ballots that do not contain clones. That means
that (matrix based) clone proof methods will protect
also other sets of candidates than sets of clones
(e.g. Smith set may or may not consist of clones).
Benham's Dominant Mutual Quarter Burial Resistance
26: A>B
25: C>A
49: B>C (sincere is B>A or B)
If these ballots were sincere, one would expect B to win
(and almost all methods elect B). However, if it's true
that the 49 voters are on a burial spree, then it would be a
bad thing to elect B. But the method can't tell which is
the case from the ballots alone.
Yes. I hope that Condorcet elections would have
relatively few strategic voters, and that their
impact would be just noise. If there are large
numbers of strategic voters (e.g. 49%) then the
system has pretty much already failed (except if
it is the intention of the method that all should
vote strategically).
In that sense, some strategy hardening is more expensive
than others. If the hardening only involves ballot
situations that would very rarely appear honestly, or if the
candidate it elects to deter strategy is only slightly worse
than that it would otherwise elect, then the hardening is
"cheap". Otherwise, it's expensive. Some
strategy hardening is next to free, I think; cases where the
strategy applies *because* the method is bad at picking
honest winners, not because it's good.
I'd like to see all the vulnerability reports
and hardening plans to be accompanied with some
analysis and/or example cases where one tries
to estimate the seriousness of the problem
against expected real life situations. Pure
theoretical examples are not good enough for
practical real life decisions.

Let me take one example. Minmax indeed may elect
Condorcet losers. But is this probable in real
life elections? I think the probability is very
very small. So, the threat is there but it has
no importance in real life elections. ((In
addition one could of course also claim that if
minmax elects a Condorcet loser it does so for
a good reason.))
There are thus different kind of environments and
different kind of
needs. One should pick the best method for each need
and environment.
Somewhere it may be e.g. FPTP or minmax(margins),
somewhere something
else.
Given the above, that's right. I can't quite see
the situation where FPTP would be preferred, except possibly
where there are only ever two choices (but most methods
reduce to FPTP in that case).
I reserved some space for interest to intentionally
base the society on a two-party model. That can be
seen as one form of democracy that does indeed work.
I'm not really a strong proponent of it but I can
understand if someone finds it to be a working
system. It has also some claimed benefits like strong
governments when compared to typical multi-party systems.
Even though I've said it before, I'll repeat my
runoff idea: to have two different methods, one very
resistant to strategy, and another good at finding honest
winners, and picking the winners from each for the runoff.
Yes, at least in theory this makes sense. In the
26-25-49 example above and with some basic Condorcet
method and IRV (with same strategic or sincere
ballots) you would elect the Condorcet winner despite
of the strategy. (It is enough to get the Condorcet
winner to the runoff from either method.)
It would be extremely complex, though (I remember one reply
saying to the effect of "You can't be
serious!"). It could also, perhaps, tempt the
population to vote more strategically since "less is on
the line", as I talked about in my message about TTR.
Yes, that is possible too. But as already said, I'd
expect many societies to lean towards strategy free
voting. And many strategies are also quite difficult
to implement in real life elections (in most societies).

One should maybe start testing different methods (that
elect good winners but that are not necessarily
maximally rigged to defend against strategies) in some
smaller elections to first gain trust that the
strategies will not be a serious problem.

Juho








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Kristofer Munsterhjelm
2008-11-27 18:33:59 UTC
Permalink
Post by Juho Laatu
I'll try to answer very shortly to most of the points.
I can comment more if there are some interesting ones.
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Tuesday, 25 November, 2008, 1:37 PM
--- On Sun, 23/11/08, Kristofer Munsterhjelm
Post by Kristofer Munsterhjelm
Regarding number two, simple Condorcet methods
exist. Borda-elimination (Nanson or Raynaud) is Condorcet.
Minmax is quite simple, and everybody who's
dealt with sports knows Copeland (with Minmax
tiebreaks). I'll partially grant this, though,
since the good methods are complex
Minmax is both simple and good. I think at least
minmax(margins) is a good solution for many needs.
The weakest spot of minmax(margins) could be that it
fails mutual majority. That means for example that
nominating a set of clones instead of just one
candidate could lead (at least in theory) to not
winning the election.
On the other hand other methods than minmax(margins)
may not respect the good idea of mmm to elect the
candidate that has the least incentive among voters
to be changed to some other of the candidates.
the candidates.
I think Schulze said that his method was the one that
agreed most with Minmax while still being cloneproof.
According to Warren, that is true (he refers to simulations
made by Petry and Heitzig) - see
http://rangevoting.org/SchulzeExplan.html .
The claim seems to be about Smith//MinMax.
Yes; so we can say it's the method that agrees most with Minmax while
being cloneproof and Smith.
Post by Juho Laatu
At the other end of "generalizable methods" you
have Kemeny. Kemeny is not cloneproof (it suffers from
crowding). I wonder what "Cloneproof Kemeny" would
look like, but there have been attempts to move Ranked Pairs
http://listas.apesol.org/pipermail/election-methods-electorama.com/2004-November/014208.html
Note that the minmax philosophy is to study paths of
length one. Minmax philosophy says that voter interest
to replace the elected candidate with another is more
relevant than their interest to replace the candidates
in chain. (Such chains of changes do not typically
happen in real life after the election.)
I'm not sure about this. The alternate description of Minmax as making
use of successive eliminations may point at it involving long paths. At
least I think that's partly the reason Schulze is so similar to Minmax
(or Smith//Minmax).
Post by Juho Laatu
(Minmax(margins) fails also Smith and Condorcet loser,
but those violations can be explained to be intentional
and positive.)
That's a problem, in my opinion. A voting method also
is a metric of who deserves to win.
Yes if one sets that as a target. The alternative is
to emphasize also other aspects like being free of
strategic voting related risks. I think minmax can be
seen as an ideal definition (for some needs) of which
candidate is best.
In that point of view,
if the metric says that Condorcet winners are good, but the
method can elect Conorcet losers, the metric is
self-contradictory.
Minmax may elect the Condorcet loser only when there
is no Condorcet winner. And only in situations where
all other candidates are worse than the Condorcet
loser from the minmax philosophy/utility point of view.
The problem is criterion compliance. Isolated, I think passing Condorcet
and failing Condorcet loser is a contradiction, because this means you
can possibly reverse the election and get a "worst" that is the "best".
I know that there are weaknesses to my argument (since others could make
the same reasoning about Consistency, for instance, and exclude all
Condorcet methods), but I think that inasfar as voting methods are
metrics of winners, and the reason for why one is supposed to use this
method is because of its criterion compliance (which is really a way of
saying certain ways of picking winners/not picking winners is
desirable), one should take the reason to its full extent, which a
method that fails Condorcet loser doesn't do.
Post by Juho Laatu
As for Smith, I would like to have that
as well, since if the method says Condorcet for a candidate,
it should also say Condorcet for a set (unless there's
some overriding strategy-proofing reason as to why not).
I don't see that as a requirement even if there were
no strategy-proofing needs. The minmax philosophy says
that voters may have more interest to replace the
elected Smith set member with another member of the
set than they have interest to replace someone outside
of that set with others.
If that is true, one should advocate Minmax on that the Minmax
philosophy is a good one, and if it meets Condorcet, that's a bonus as
well, but that it's the Minmax philosophy that is paramount.

Smith isn't just a hardening criterion. In a sense, it also assures
voters that they can vote in a way they want without having to
compensate in order to get a candidate from the Smith (or mutual
majority, etc) set, if all other voters are honest. In this way, it
would be similar to independence of clones: a cloneproof method tells
voters that now it matters much less whether candidates are loosely
spread or tightly clumped around an area, even if the candidates were
clumped/spread apart simply because of the political environment (and
through no adverse intent nor strategic nomination).
Post by Juho Laatu
Also minmax(margins) is close to this. It has a very
natural explanation. (I gave one rough explanation
above. Another one is "elect the candidate that needs
least additional votes to win all others".)
Kemeny is also quite simple, I suppose. It's merely
"Find the ordering where most people agree with the
preferences".
One could see Kemeny as a good definition of a good
social ordering. That may or may not correlate with
the definition of the best single winner.
If the concept of a social ordering is to have any use, I think the
winner must be first on it. It could be otherwise if there was a
splitting effect (like the PR "0.5 for single winner, 0.25 and 0.75 for
two winners" case), but I can't quite see how that would be the case.
Post by Juho Laatu
Yes. One has to guess, or one may modify the system when
one sees the level of strategic voting and its level of
impact. In general I believe strategic voting would not
be as bad as discussions on this list might suggest.
Take for example all the numerous Top Two Runoff
elections today. People speculate on strategic
possibilities and other problems only afterwards but
in most cases they vote sincerely in the elections.
That may be true; even a method like Bucklin seemed to support a
somewhat competitive environment (at least to the extent that one of the
candidates who didn't win were strong enough to go to court about it).
But we don't really know; while we can program our computers to make
millions of ballot simulations, we can't simulate the voters. All we
have to go on, as such, is the ballot data (which can be warped by
strategic incentive) and observations like yours.

Say we were going to make a "Organization for Condorcet Voting".
Advocating multiple Condorcet methods would probably "split the vote" as
it were (considering the usual state of things as Plurality). That's
what some IRV supporters say about Condorcet itself (to my knowledge),
that we should support IRV and then possibly go to Condorcet later
rather than fragment electoral reform. So which will it be? What we have
to go on is, on one hand, the theoretical measures, and on the other, a
few pieces of data. It's not going to be easy...
Post by Juho Laatu
One way to deal with this is to make the method maximally
safe against strategy. However, for some types of strategy
this makes the method return worse results were the voters
honest. Say there's an election where the
"unaugmented winner" is X. If the method is
strategy-hardened, the winner will be Y instead. Then there
may be an instance in which people truly wanted X, but also
another instance where the people truly wanted Y but some
employed strategy. The method can't read people's
minds and thus can't know which is the case, which means
that any case of the former would lead to a worse result if
the method was strategy-hardened.
Yes, there is always a trade-off. Maybe it is a worse
failure to elect a wrong winner due to a successful
strategic plot than due to a method that doesn't
always elect the best winner. But failure to elect
the best possible winner with sincere votes is a
serious problem too.
One observation about clones. One can get the same
pairwise matrix from ballots that contain clones and
from ballots that do not contain clones. That means
that (matrix based) clone proof methods will protect
also other sets of candidates than sets of clones
(e.g. Smith set may or may not consist of clones).
What do you mean by that the you can get the same matrix from ballots
with and without clones? I assume you mean something like that if you
have a ballot specifying A1>A2>A3>B, you can derive the A*>B preference
as it would have been even without A2 and A3. That's true. But consider
a very simple method that just looks for clones and removes them; that
would remove only the clones (although it would be extremely brittle and
hence not very useful). Could such a method be implemented on matrices
alone? If all clones are in the same direction, then yes.. I'm not sure
about the case where they're in random order, though. Perhaps you're
right, or maybe you can detect clones in random order as well; perhaps
something like "if for all A in some subset, for all others B, either
A>B or B>A with the exact same number of voters, then that subset
consists of clones".
Post by Juho Laatu
Benham's Dominant Mutual Quarter Burial Resistance
26: A>B
25: C>A
49: B>C (sincere is B>A or B)
If these ballots were sincere, one would expect B to win
(and almost all methods elect B). However, if it's true
that the 49 voters are on a burial spree, then it would be a
bad thing to elect B. But the method can't tell which is
the case from the ballots alone.
Yes. I hope that Condorcet elections would have
relatively few strategic voters, and that their
impact would be just noise. If there are large
numbers of strategic voters (e.g. 49%) then the
system has pretty much already failed (except if
it is the intention of the method that all should
vote strategically).
I agree. About the only ways I can think of this happening for a public
election would be through vote management or through extreme incentives
to bury (on the order of FPTP's incentive to vote for frontrunners). I
think Benham's point was to have an example where one could say
something to the effect of "if the method resists this burial, then it
resists any realistic burial as well"; or in the case of the
Copeland-ish variant from which this was taken, "the method resists
burial extremely well, so burial (of this kind) will be no problem anymore".
Post by Juho Laatu
In that sense, some strategy hardening is more expensive
than others. If the hardening only involves ballot
situations that would very rarely appear honestly, or if the
candidate it elects to deter strategy is only slightly worse
than that it would otherwise elect, then the hardening is
"cheap". Otherwise, it's expensive. Some
strategy hardening is next to free, I think; cases where the
strategy applies *because* the method is bad at picking
honest winners, not because it's good.
I'd like to see all the vulnerability reports
and hardening plans to be accompanied with some
analysis and/or example cases where one tries
to estimate the seriousness of the problem
against expected real life situations. Pure
theoretical examples are not good enough for
practical real life decisions.
Let me take one example. Minmax indeed may elect
Condorcet losers. But is this probable in real
life elections? I think the probability is very
very small. So, the threat is there but it has
no importance in real life elections. ((In
addition one could of course also claim that if
minmax elects a Condorcet loser it does so for
a good reason.))
This is going to be hard, for the reasons I showed earlier. But it's a
good point: if we can get data based on real life situations, then those
are definitely preferrable to others.

Though there's always the chance that if we were to set up an
Organization for Condorcet Voting, IRV or FPTP supporters would say
something like "they say IRV is nonmonotonic, well, this thing can't
even make up its mind what the true winner should be!" (regarding
Reversal symmetry). That's one way theoretical issues, even those that
don't really matter in real life elections, could come into play. (Of
course, one could then respond that "IRV squeezes the center and FPTP
explodes said center, but Condorcet supports the center", for instance.
I'm using general statements here - they may not fit completely, but you
see the idea.
Post by Juho Laatu
Even though I've said it before, I'll repeat my
runoff idea: to have two different methods, one very
resistant to strategy, and another good at finding honest
winners, and picking the winners from each for the runoff.
Yes, at least in theory this makes sense. In the
26-25-49 example above and with some basic Condorcet
method and IRV (with same strategic or sincere
ballots) you would elect the Condorcet winner despite
of the strategy. (It is enough to get the Condorcet
winner to the runoff from either method.)
It would be extremely complex, though (I remember one reply
saying to the effect of "You can't be
serious!"). It could also, perhaps, tempt the
population to vote more strategically since "less is on
the line", as I talked about in my message about TTR.
Yes, that is possible too. But as already said, I'd
expect many societies to lean towards strategy free
voting. And many strategies are also quite difficult
to implement in real life elections (in most societies).
One should maybe start testing different methods (that
elect good winners but that are not necessarily
maximally rigged to defend against strategies) in some
smaller elections to first gain trust that the
strategies will not be a serious problem.
Yes, or implement them into programs that can be used for informal
voting or voting on websites or in similar situations. I think the
voting program mentioned here some time ago (Selectricity?) aims towards
the latter.
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Juho Laatu
2008-11-28 00:01:14 UTC
Permalink
Post by Kristofer Munsterhjelm
Post by Juho Laatu
Note that the minmax philosophy is to study paths of
length one. Minmax philosophy says that voter interest
to replace the elected candidate with another is more
relevant than their interest to replace the candidates
in chain. (Such chains of changes do not typically
happen in real life after the election.)
I'm not sure about this. The alternate description of
Minmax as making use of successive eliminations may point at
it involving long paths. At least I think that's partly
the reason Schulze is so similar to Minmax (or
Smith//Minmax).
I didn't quite get this. When evaluating
candidate X minmax just checks if voters
would be interested in changing X to some
other candidate (in one step), while
methods like Schulze and Ranked Pairs may
base their evaluation on chains of victories
leading to X.
Post by Kristofer Munsterhjelm
Post by Juho Laatu
Minmax may elect the Condorcet loser only when there
is no Condorcet winner. And only in situations where
all other candidates are worse than the Condorcet
loser from the minmax philosophy/utility point of
view.
The problem is criterion compliance. Isolated, I think
passing Condorcet and failing Condorcet loser is a
contradiction, because this means you can possibly reverse
the election and get a "worst" that is the
"best". I know that there are weaknesses to my
argument (since others could make the same reasoning about
Consistency, for instance, and exclude all Condorcet
methods), but I think that inasfar as voting methods are
metrics of winners, and the reason for why one is supposed
to use this method is because of its criterion compliance
(which is really a way of saying certain ways of picking
winners/not picking winners is desirable), one should take
the reason to its full extent, which a method that fails
Condorcet loser doesn't do.
There are different kind of criteria.
If one decides the winner based on one single
vote a method that would elect the least
preferred candidate would be bad. Things get
however more complex with group opinions that
may contain cycles. Then it is possible that
some candidate loses to every other candidate
but still is the most liked one in the sense
that there is only a very weak interest to
change that candidate to some other candidate.
Post by Kristofer Munsterhjelm
Post by Juho Laatu
As for Smith, I would like to have that
as well, since if the method says Condorcet for a
candidate,
Post by Juho Laatu
it should also say Condorcet for a set (unless
there's
Post by Juho Laatu
some overriding strategy-proofing reason as to why
not).
Post by Juho Laatu
I don't see that as a requirement even if there
were
Post by Juho Laatu
no strategy-proofing needs. The minmax philosophy says
that voters may have more interest to replace the
elected Smith set member with another member of the
set than they have interest to replace someone outside
of that set with others.
If that is true, one should advocate Minmax on that the
Minmax philosophy is a good one, and if it meets Condorcet,
that's a bonus as well, but that it's the Minmax
philosophy that is paramount.
Yes, I assumed that in this case the society
had chosen minmax as a sincere utility
function that determines the best winner.
Post by Kristofer Munsterhjelm
Smith isn't just a hardening criterion. In a sense, it
also assures voters that they can vote in a way they want
without having to compensate in order to get a candidate
from the Smith (or mutual majority, etc) set, if all other
voters are honest. In this way, it would be similar to
independence of clones: a cloneproof method tells voters
that now it matters much less whether candidates are loosely
spread or tightly clumped around an area, even if the
candidates were clumped/spread apart simply because of the
political environment (and through no adverse intent nor
strategic nomination).
I can see two kind of reasoning that people
may use to justify the use of Smith set as
a criterion that determines the best winner.

1) Clone based. Smith set is some sort of an
approximation of clone candidates. Smith set
is however wider (wider than the set of
candidates that are next to each others in
every ballot). (Note also that candidates
that are next to each others in every ballot
need not be clones in the sense that they
would be ideologically similar.)

2) Drawing technique based. When drawing a
graph that represents the results of the
election one typically draws the Smith set
candidates at the top of the paper, and all
the other candidates below that group. Since
people intuitively model also group opinions
as linear preference chains this drawing
technique may give them a false impression of
the group preferences. The problem is that
this drawing technique hides the defeats of
the Smith set members to each others.
Post by Kristofer Munsterhjelm
Post by Juho Laatu
One could see Kemeny as a good definition of a good
social ordering. That may or may not correlate with
the definition of the best single winner.
If the concept of a social ordering is to have any use, I
think the winner must be first on it.
My statement was not quite accurate. I should
have said only that the criteria for
determining the social ordering and the best
winner in some single-winner election may be
different.
Post by Kristofer Munsterhjelm
Say we were going to make a "Organization for
Condorcet Voting". Advocating multiple Condorcet
methods would probably "split the vote" as it were
(considering the usual state of things as Plurality).
That's what some IRV supporters say about Condorcet
itself (to my knowledge), that we should support IRV and
then possibly go to Condorcet later rather than fragment
electoral reform. So which will it be? What we have to go on
is, on one hand, the theoretical measures, and on the other,
a few pieces of data. It's not going to be easy...
I think it would be good to agree on the
target first. For example the target of
making U.S. a multi-party democracy is quite
different from the target of removing the
problem of small party spoilers in the
presidential elections. And promotion of
one's favourite method at all cost is yet
another quite different target.
Post by Kristofer Munsterhjelm
Post by Juho Laatu
One observation about clones. One can get the same
pairwise matrix from ballots that contain clones and
from ballots that do not contain clones. That means
that (matrix based) clone proof methods will protect
also other sets of candidates than sets of clones
(e.g. Smith set may or may not consist of clones).
What do you mean by that the you can get the same matrix
from ballots with and without clones?
Here's an example of what I was thinking.

2: A>B>C>D
2: B>C>A>D
2: C>A>B>D
1: D>A>B>C
1: D>B>C>A
1: D>C>A>B

A, B and C are clones in the sense that they
are next to each others in every ballot. A, B
and C also form a Smith set.

3: A>B>D>C
3: B>C>D>A
3: C>A>D>B

With these ballots the resulting matrix (and
Smith set) is exactly the same. But A, B and
C are not next to each others in any of the
ballots.
Post by Kristofer Munsterhjelm
I assume you mean
something like that if you have a ballot specifying
A1>A2>A3>B, you can derive the A*>B preference
as it would have been even without A2 and A3. That's
true. But consider a very simple method that just looks for
clones and removes them; that would remove only the clones
(although it would be extremely brittle and hence not very
useful). Could such a method be implemented on matrices
alone? If all clones are in the same direction, then yes..
I'm not sure about the case where they're in random
order, though. Perhaps you're right, or maybe you can
detect clones in random order as well; perhaps something
like "if for all A in some subset, for all others B,
either A>B or B>A with the exact same number of
voters, then that subset consists of clones".
As demonstrated above clones (as typically
defined) can not be derived from the matrix
alone. Also ballots are needed.

Yes, one could replace sets of clones with
some virtual candidate. If that virtual
candidate wins then one can use some further
"completion method" to determine the winner
within that clone set.

I have also played with the idea of allowing
the candidates themselves to indicate which
of them should be treated as clones. That
would guarantee that all clones and only
clones are treated as clones.

(One could go also further and allow
hierarchies of clone groups.)
Post by Kristofer Munsterhjelm
Post by Juho Laatu
Yes. I hope that Condorcet elections would have
relatively few strategic voters, and that their
impact would be just noise. If there are large
numbers of strategic voters (e.g. 49%) then the
system has pretty much already failed (except if
it is the intention of the method that all should
vote strategically).
I agree. About the only ways I can think of this happening
for a public election would be through vote management or
through extreme incentives to bury (on the order of
FPTP's incentive to vote for frontrunners).
In Condorcet vote management could be the
most probable path leading to "too high
levels" of strategic voting. In large public
elections with independent voters the risks
are at rather low level.
Post by Kristofer Munsterhjelm
Though there's always the chance that if we were to set
up an Organization for Condorcet Voting, IRV or FPTP
supporters would say something like "they say IRV is
nonmonotonic, well, this thing can't even make up its
mind what the true winner should be!" (regarding
Reversal symmetry). That's one way theoretical issues,
even those that don't really matter in real life
elections, could come into play. (Of course, one could then
respond that "IRV squeezes the center and FPTP explodes
said center, but Condorcet supports the center", for
instance. I'm using general statements here - they may
not fit completely, but you see the idea.
My theoretical approach to the problem of
having many different Condorcet (and other)
methods is that there may be many utility
functions that one may choose. In some cases
there might also be a need to strengthen the
methods and make them more strategy resistant
(at the cost of not always electing the best
winner according to the agreed utility
function).

My practical approach might be to pick a
representative set of Condorcet methods and
say that they are all good.

These election method evaluation questions
are tricky. It is very difficult to explain
all the relevant factors. And on the other
hand it is easy to develop various threat
scenarios that can be used against other
methods.

A unified front of respected experts could do
a lot. Unfortunately all the experts seem to
have their own favourite methods and
corresponding campaigns :-).
Post by Kristofer Munsterhjelm
Post by Juho Laatu
One should maybe start testing different methods (that
elect good winners but that are not necessarily
maximally rigged to defend against strategies) in some
smaller elections to first gain trust that the
strategies will not be a serious problem.
Yes, or implement them into programs that can be used for
informal voting or voting on websites or in similar
situations. I think the voting program mentioned here some
time ago (Selectricity?) aims towards the latter.
Yes, that is a good approach that introduces
new good methods to the voters. One could
market these services also to TV shows etc.
to get lots of publicity and experience in
large elections. That would demonstrate the
viability of these methods (and ability to
cast sincere and informative votes without
any strategic voting related needs and fears)
also for use in political elections.

Juho







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Kristofer Munsterhjelm
2008-12-01 11:28:42 UTC
Permalink
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Post by Juho Laatu
Minmax may elect the Condorcet loser only when there
is no Condorcet winner. And only in situations where
all other candidates are worse than the Condorcet
loser from the minmax philosophy/utility point of
view.
The problem is criterion compliance. Isolated, I think
passing Condorcet and failing Condorcet loser is a
contradiction, because this means you can possibly reverse
the election and get a "worst" that is the
"best". I know that there are weaknesses to my
argument (since others could make the same reasoning about
Consistency, for instance, and exclude all Condorcet
methods), but I think that inasfar as voting methods are
metrics of winners, and the reason for why one is supposed
to use this method is because of its criterion compliance
(which is really a way of saying certain ways of picking
winners/not picking winners is desirable), one should take
the reason to its full extent, which a method that fails
Condorcet loser doesn't do.
There are different kind of criteria.
If one decides the winner based on one single
vote a method that would elect the least
preferred candidate would be bad. Things get
however more complex with group opinions that
may contain cycles. Then it is possible that
some candidate loses to every other candidate
but still is the most liked one in the sense
that there is only a very weak interest to
change that candidate to some other candidate.
Then you should advocate Minmax for being Minmax, not for being
Condorcet compliant. If you do the latter, then people may argue that
the system is inconsistent because it doesn't follow up the implication
of Condorcet (Condorcet loser, etc). But to my knowledge, you want to do
the former, so I won't comment on this.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Smith isn't just a hardening criterion. In a sense, it
also assures voters that they can vote in a way they want
without having to compensate in order to get a candidate
from the Smith (or mutual majority, etc) set, if all other
voters are honest. In this way, it would be similar to
independence of clones: a cloneproof method tells voters
that now it matters much less whether candidates are loosely
spread or tightly clumped around an area, even if the
candidates were clumped/spread apart simply because of the
political environment (and through no adverse intent nor
strategic nomination).
I can see two kind of reasoning that people
may use to justify the use of Smith set as
a criterion that determines the best winner.
1) Clone based. Smith set is some sort of an
approximation of clone candidates. Smith set
is however wider (wider than the set of
candidates that are next to each others in
every ballot). (Note also that candidates
that are next to each others in every ballot
need not be clones in the sense that they
would be ideologically similar.)
2) Drawing technique based. When drawing a
graph that represents the results of the
election one typically draws the Smith set
candidates at the top of the paper, and all
the other candidates below that group. Since
people intuitively model also group opinions
as linear preference chains this drawing
technique may give them a false impression of
the group preferences. The problem is that
this drawing technique hides the defeats of
the Smith set members to each others.
I would have two reasons as well, but none of those you mentioned. It's
possible to be cloneproof without being Smith and vice versa..

1. Logical endpoint of mutual majority. A mutual majority set is one
that a majority prefers to all else. Now consider a mutual dominant nth
set. A mutual dominant nth set is a set that 1/n of all voters prefer to
all the others, and where one of the candidates within wins, pairwise.
Smith is just mutual dominant set with n->inf.

2. Condorcet for sets. Smith is Condorcet for sets. If a set can beat
all those outside the set pairwise, it should win. If the set is of size
one, well, that's just Condorcet. The only reason why it should hold for
size one, but not, say, size two, is if some other heuristic (like the
Minmax metric/utility heuristic) is more important. If it is, see my
first paragraph; but if we want this method primarily because it's
Condorcet, or because the Condorcet idea itself is a good one, then we
should be consistent and take that Condorcet as far as possible.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Post by Juho Laatu
One could see Kemeny as a good definition of a good
social ordering. That may or may not correlate with
the definition of the best single winner.
If the concept of a social ordering is to have any use, I
think the winner must be first on it.
My statement was not quite accurate. I should
have said only that the criteria for
determining the social ordering and the best
winner in some single-winner election may be
different.
In what situations would the single winner and the social ordering
differ? It does, for proportional completion (because that's
proportional and thus PR-esque thinking appllies), but to majority
methods... I can't quite see when that would be the case.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Say we were going to make a "Organization for
Condorcet Voting". Advocating multiple Condorcet
methods would probably "split the vote" as it were
(considering the usual state of things as Plurality).
That's what some IRV supporters say about Condorcet
itself (to my knowledge), that we should support IRV and
then possibly go to Condorcet later rather than fragment
electoral reform. So which will it be? What we have to go on
is, on one hand, the theoretical measures, and on the other,
a few pieces of data. It's not going to be easy...
I think it would be good to agree on the
target first. For example the target of
making U.S. a multi-party democracy is quite
different from the target of removing the
problem of small party spoilers in the
presidential elections. And promotion of
one's favourite method at all cost is yet
another quite different target.
The CVD (FairVote) tries to do both. In one sense, that may be why they
got stuck with IRV in the first place, though now I think that it's at
least in part because of their (CVD's) partly undemocratic nature. In
any event, it might be good to have a plan for both, or they could say
"we want both multiwinner and singlewinner change, they have just one".
Perhaps that's not very likely, but still... which of course leads to
the question of what a multiwinner method that reduces to Condorcet in
the single-winner case yet runs in polytime would look like.

In any event, if we want to "hit the ground running", then you're right,
instead of inventing a united method, we should focus on one or the
other. I think QPQ would be a good multiwinner method, but to my
knowledge, it reduces to IRV. I also haven't checked if there are any
"automatically disqualifying failures", like MMPO's Plurality failure.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Post by Juho Laatu
One observation about clones. One can get the same
pairwise matrix from ballots that contain clones and
from ballots that do not contain clones. That means
that (matrix based) clone proof methods will protect
also other sets of candidates than sets of clones
(e.g. Smith set may or may not consist of clones).
What do you mean by that the you can get the same matrix
from ballots with and without clones?
Here's an example of what I was thinking.
2: A>B>C>D
2: B>C>A>D
2: C>A>B>D
1: D>A>B>C
1: D>B>C>A
1: D>C>A>B
A, B and C are clones in the sense that they
are next to each others in every ballot. A, B
and C also form a Smith set.
3: A>B>D>C
3: B>C>D>A
3: C>A>D>B
With these ballots the resulting matrix (and
Smith set) is exactly the same. But A, B and
C are not next to each others in any of the
ballots.
Well, if we're cloneproof, it doesn't matter (from the point of view of
the cloneproof criterion) which of the clones we pick when we pick among
the clones, if the clone set won. So the method might pick the candidate
that would be the most suitable one if the set wasn't a clone set, and
that way it only goes against the objective of picking the most suitable
winner when to do otherwise would make it no longer cloneproof -- kind
of like Schulze's weak invulnerability to Hylland free riding, saying in
effect "a method passing this is only vulnerable to Hylland free riding
when not being would make it fail the DPC".
Post by Juho Laatu
As demonstrated above clones (as typically
defined) can not be derived from the matrix
alone. Also ballots are needed.
Yes, one could replace sets of clones with
some virtual candidate. If that virtual
candidate wins then one can use some further
"completion method" to determine the winner
within that clone set.
I have also played with the idea of allowing
the candidates themselves to indicate which
of them should be treated as clones. That
would guarantee that all clones and only
clones are treated as clones.
(One could go also further and allow
hierarchies of clone groups.)
It's easy to make a voting method "cloneproof" in this manner. Just have
a prefix that collapses clones down to single candidates, then if any of
those pseudocandidates win, pick the one that's closest to winning were
the clone candidates not collapsed. But that would be a very fragile
cloneproof condition indeed.

Consider something like this:

1000: A>B>C>D>E
1021: D>A>B>C>E
874: E>D>A>B>C
760: C>B>A>D>E

(Schulze gives D > A > B > C > E)

{A,B,C} are clones, and the prefix method would replace them with a
candidate of its own. But now consider this:

1000: A>B>C>D>E
1021: D>A>B>C>E
874: E>D>A>B>C
760: C>B>A>D>E
1: C>D>B>E>A

(Schulze still gives D > A > B > C > E)

Now they're not strict clones anymore. A good method should recover
gracefully from this condition, since in real world elections, it's very
unlikely that all voters would vote the clones exactly in the way to
make them obvious as clones. The prefix wouldn't do that.
Post by Juho Laatu
In Condorcet vote management could be the
most probable path leading to "too high
levels" of strategic voting. In large public
elections with independent voters the risks
are at rather low level.
Do you mean the risks from vote management, or non-vote-management strategy?
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Though there's always the chance that if we were to set
up an Organization for Condorcet Voting, IRV or FPTP
supporters would say something like "they say IRV is
nonmonotonic, well, this thing can't even make up its
mind what the true winner should be!" (regarding
Reversal symmetry). That's one way theoretical issues,
even those that don't really matter in real life
elections, could come into play. (Of course, one could then
respond that "IRV squeezes the center and FPTP explodes
said center, but Condorcet supports the center", for
instance. I'm using general statements here - they may
not fit completely, but you see the idea.
My theoretical approach to the problem of
having many different Condorcet (and other)
methods is that there may be many utility
functions that one may choose. In some cases
there might also be a need to strengthen the
methods and make them more strategy resistant
(at the cost of not always electing the best
winner according to the agreed utility
function).
My practical approach might be to pick a
representative set of Condorcet methods and
say that they are all good.
These election method evaluation questions
are tricky. It is very difficult to explain
all the relevant factors. And on the other
hand it is easy to develop various threat
scenarios that can be used against other
methods.
A unified front of respected experts could do
a lot. Unfortunately all the experts seem to
have their own favourite methods and
corresponding campaigns :-).
That was a reference to Minmax. If you throw nonmonotonicity at IRV,
they might throw reversal symmetry failure at you in return. This could
happen even with the kind of criteria we think are not very important
(Consistency, Participation, or LNH* for a method that fails both LNHs),
but it would carry greater weight for those criteria that are meaningful
("they say IRV spoils candidates, but with Nanson, it's not even
cloneproof!" or whatever).

As for experts, again we hit the problem of estimating how much strategy
would happen. Ideally, we'd either have that data or we'd have some way
of saying "all we mean is that Condorcet is good: if you want something
good but possibly complex, choose this, otherwise..", and unite under
Condorcet. Perhaps some sort of "here's the criteria the different
methods pass, pick what you think would be best", but I think knowing
real world strategy so we could find a single Condorcet method would be
better.
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Juho Laatu
2008-12-03 05:34:38 UTC
Permalink
Post by Kristofer Munsterhjelm
Post by Juho Laatu
There are different kind of criteria.
If one decides the winner based on one single
vote a method that would elect the least
preferred candidate would be bad. Things get
however more complex with group opinions that
may contain cycles. Then it is possible that
some candidate loses to every other candidate
but still is the most liked one in the sense
that there is only a very weak interest to
change that candidate to some other candidate.
Then you should advocate Minmax for being Minmax, not for
being Condorcet compliant. If you do the latter, then people
may argue that the system is inconsistent because it
doesn't follow up the implication of Condorcet
(Condorcet loser, etc). But to my knowledge, you want to do
the former, so I won't comment on this.
I don't have any strong promotional interests.
I like clarity and clear understanding. In this
case there is no need to refer to Condorcet
compatibility since Minmax(margins) can be
defined well (maybe better) without it.

Also the fact that the Condorcet winner vs.
Condorcet loser question is tricky may be a
reason to describe the method as Minmax. But
in general I do not fancy the idea of using
verbal tricks to make something look better
or worse than it is.

I'm thus ok with any definition. Minmax as
Minmax sounds good.

On the other hand minmax is a mathematical
term and adding "margins" there makes it
even more complex. For this reason also e.g.
"least additional votes", "least interest to
change" or "best pairwise result" based
names or short abbreviations could be ok
(for use outside the EM expert community).
Post by Kristofer Munsterhjelm
Post by Juho Laatu
I can see two kind of reasoning that people
may use to justify the use of Smith set as
a criterion that determines the best winner.
1) Clone based. Smith set is some sort of an
approximation of clone candidates. Smith set
is however wider (wider than the set of
candidates that are next to each others in
every ballot). (Note also that candidates
that are next to each others in every ballot
need not be clones in the sense that they
would be ideologically similar.)
2) Drawing technique based. When drawing a
graph that represents the results of the
election one typically draws the Smith set
candidates at the top of the paper, and all
the other candidates below that group. Since
people intuitively model also group opinions
as linear preference chains this drawing
technique may give them a false impression of
the group preferences. The problem is that
this drawing technique hides the defeats of
the Smith set members to each others.
I would have two reasons as well, but none of those you
mentioned. It's possible to be cloneproof without being
Smith and vice versa..
1. Logical endpoint of mutual majority. A mutual majority
set is one that a majority prefers to all else. Now consider
a mutual dominant nth set. A mutual dominant nth set is a
set that 1/n of all voters prefer to all the others, and
where one of the candidates within wins, pairwise. Smith is
just mutual dominant set with n->inf.
2. Condorcet for sets. Smith is Condorcet for sets. If a
set can beat all those outside the set pairwise, it should
win. If the set is of size one, well, that's just
Condorcet. The only reason why it should hold for size one,
but not, say, size two, is if some other heuristic (like the
Minmax metric/utility heuristic) is more important. If it
is, see my first paragraph; but if we want this method
primarily because it's Condorcet, or because the
Condorcet idea itself is a good one, then we should be
consistent and take that Condorcet as far as possible.
The mutual majority criterion is related to clones.
But it can also be seen as a criterion that refers
to the majority rule and life after the election.
I mean that some majority group may say after the
election "we want these candidates to win" and it
is difficult to explain that they will not get what
they want since they had conflicting opinions within
that candidate set on which one of them should win.

"Condorcet for sets" sounds a bit "aesthetics based"
to me since I don't know what practical real life
situation (other than aesthetic observations on the
graph that describes the pairwise preferences) could
be used to justify this criterion. If that set was
one candidate (or a nominated party/grouping) then
the basic Condorcet rule would apply, but if the
Smith set is just a random set of candidates and
there is no single majority group of voters behind
this group opinion then it is harder to find the
rationale. (The set members may not be clones and
there may not be a single set of voters that think
that this set is better than others.)

One should also ask if the clone criterion is ideal.
For strategy reasons sufficient independence of
clones may be necessary to make it safe for
parties/wings to nominate more than one candidate
(or to nominate only one).

How about the following situation. Both Democrats
and Republicans have three clone candidates. All
votes are sincere. Both parties have 50% support.
The Democrat candidates have a clear group
preference order. The Republican candidates are
badly looped. Is the fact that electing a
Republican candidate would leave us in a
situation where majority of the voters are
not happy but would like to replace this
candidate with another candidate a sufficient
reason to elect the best Democrat candidate
instead. I.e. should we be fully independent of
clones or should we elect the candidate that
seems to be the best compromise candidate /
most agreeable (=least opposition in any
pairwise comparison)?
Post by Kristofer Munsterhjelm
In what situations would the single winner and the social
ordering differ? It does, for proportional completion
(because that's proportional and thus PR-esque thinking
appllies), but to majority methods... I can't quite see
when that would be the case.
No need to be different. I was just thinking
that they may be used for different purposes
and therefore may be different.
Post by Kristofer Munsterhjelm
Post by Juho Laatu
As demonstrated above clones (as typically
defined) can not be derived from the matrix
alone. Also ballots are needed.
Yes, one could replace sets of clones with
some virtual candidate. If that virtual
candidate wins then one can use some further
"completion method" to determine the winner
within that clone set.
I have also played with the idea of allowing
the candidates themselves to indicate which
of them should be treated as clones. That
would guarantee that all clones and only
clones are treated as clones.
(One could go also further and allow
hierarchies of clone groups.)
It's easy to make a voting method
"cloneproof" in this manner. Just have a prefix
that collapses clones down to single candidates, then if any
of those pseudocandidates win, pick the one that's
closest to winning were the clone candidates not collapsed.
But that would be a very fragile cloneproof condition
indeed.
1000: A>B>C>D>E
1021: D>A>B>C>E
874: E>D>A>B>C
760: C>B>A>D>E
(Schulze gives D > A > B > C > E)
{A,B,C} are clones, and the prefix method would replace
1000: A>B>C>D>E
1021: D>A>B>C>E
874: E>D>A>B>C
760: C>B>A>D>E
1: C>D>B>E>A
(Schulze still gives D > A > B > C > E)
Now they're not strict clones anymore. A good method
should recover gracefully from this condition, since in real
world elections, it's very unlikely that all voters
would vote the clones exactly in the way to make them
obvious as clones. The prefix wouldn't do that.
Yes, methods should not identify clones strictly
as in the clone definition. The transitions should
typically be smooth.

There are many ways to identify the clones.
Beatpaths is one approach. Another solution
would be e.g. to allow the candidates to
declare themselves as clones.
Post by Kristofer Munsterhjelm
Post by Juho Laatu
In Condorcet vote management could be the
most probable path leading to "too high
levels" of strategic voting. In large public
elections with independent voters the risks
are at rather low level.
Do you mean the risks from vote management, or
non-vote-management strategy?
I was thinking something like the Australian
situation where voters are used to vote as told
by the parties in the how-to-vote cards. This
makes it possible to apply strategies that would
not be possible with voters that make independent
(heterogeneous) decisions.
Post by Kristofer Munsterhjelm
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Though there's always the chance that if we
were to set
Post by Juho Laatu
Post by Kristofer Munsterhjelm
up an Organization for Condorcet Voting, IRV or
FPTP
Post by Juho Laatu
Post by Kristofer Munsterhjelm
supporters would say something like "they say
IRV is
Post by Juho Laatu
Post by Kristofer Munsterhjelm
nonmonotonic, well, this thing can't even make
up its
Post by Juho Laatu
Post by Kristofer Munsterhjelm
mind what the true winner should be!"
(regarding
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Reversal symmetry). That's one way theoretical
issues,
Post by Juho Laatu
Post by Kristofer Munsterhjelm
even those that don't really matter in real
life
Post by Juho Laatu
Post by Kristofer Munsterhjelm
elections, could come into play. (Of course, one
could then
Post by Juho Laatu
Post by Kristofer Munsterhjelm
respond that "IRV squeezes the center and
FPTP explodes
Post by Juho Laatu
Post by Kristofer Munsterhjelm
said center, but Condorcet supports the
center", for
Post by Juho Laatu
Post by Kristofer Munsterhjelm
instance. I'm using general statements here -
they may
Post by Juho Laatu
Post by Kristofer Munsterhjelm
not fit completely, but you see the idea.
My theoretical approach to the problem of
having many different Condorcet (and other)
methods is that there may be many utility
functions that one may choose. In some cases
there might also be a need to strengthen the
methods and make them more strategy resistant
(at the cost of not always electing the best
winner according to the agreed utility
function).
My practical approach might be to pick a
representative set of Condorcet methods and
say that they are all good.
These election method evaluation questions
are tricky. It is very difficult to explain
all the relevant factors. And on the other
hand it is easy to develop various threat
scenarios that can be used against other
methods.
A unified front of respected experts could do
a lot. Unfortunately all the experts seem to
have their own favourite methods and
corresponding campaigns :-).
That was a reference to Minmax. If you throw
nonmonotonicity at IRV, they might throw reversal symmetry
failure at you in return.
I wouldn't mind that since I don't see reversal
symmetry as a requirement for group opinions on
single winners. I sort of expect the society to
be mature enough to handle also the tricky
questions in some rational way.

There are many viewpoints in the comparison.
1) True targets (which candidate should be
elected, PR, regional proportionality)
2) Strategic opportunities (or the lack or
insignificance of them, or need to fix some
current problems)
3) Political realities (required steps from
the current system, risk of electing outside
of the current major players)
4) Popular claims, positive and negative
descriptions and example cases, tuned
terminology, strong persons with strong
opinions
Post by Kristofer Munsterhjelm
This could happen even with the
kind of criteria we think are not very important
(Consistency, Participation, or LNH* for a method that fails
both LNHs), but it would carry greater weight for those
criteria that are meaningful ("they say IRV spoils
candidates, but with Nanson, it's not even
cloneproof!" or whatever).
As for experts, again we hit the problem of estimating how
much strategy would happen. Ideally, we'd either have
that data or we'd have some way of saying "all we
mean is that Condorcet is good: if you want something good
but possibly complex, choose this, otherwise..", and
unite under Condorcet. Perhaps some sort of "here's
the criteria the different methods pass, pick what you think
would be best", but I think knowing real world strategy
so we could find a single Condorcet method would be better.
I'd appreceate e.g. a web site that would aim at
neutral description of all the relevant methods
(plausible candidates for election reforms), with
estimates on how they would perform in real life.

Juho









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Kristofer Munsterhjelm
2008-12-05 20:16:21 UTC
Permalink
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Then you should advocate Minmax for being Minmax, not for
being Condorcet compliant. If you do the latter, then people
may argue that the system is inconsistent because it
doesn't follow up the implication of Condorcet
(Condorcet loser, etc). But to my knowledge, you want to do
the former, so I won't comment on this.
I don't have any strong promotional interests.
I like clarity and clear understanding. In this
case there is no need to refer to Condorcet
compatibility since Minmax(margins) can be
defined well (maybe better) without it.
Also the fact that the Condorcet winner vs.
Condorcet loser question is tricky may be a
reason to describe the method as Minmax. But
in general I do not fancy the idea of using
verbal tricks to make something look better
or worse than it is.
I'm thus ok with any definition. Minmax as
Minmax sounds good.
On the other hand minmax is a mathematical
term and adding "margins" there makes it
even more complex. For this reason also e.g.
"least additional votes", "least interest to
change" or "best pairwise result" based
names or short abbreviations could be ok
(for use outside the EM expert community).
Alright. You may like Minmax for being Minmax, and that's okay; but in
my case, I'm not sure if it would withstand strategy (there's that "hard
to estimate the amount of strategy that will happen" again), and the
Minmax heuristic itself doesn't seem important enough to trade things
like clone independence and Smith for.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
I would have two reasons as well, but none of those you
mentioned. It's possible to be cloneproof without being
Smith and vice versa..
1. Logical endpoint of mutual majority. A mutual majority
set is one that a majority prefers to all else. Now consider
a mutual dominant nth set. A mutual dominant nth set is a
set that 1/n of all voters prefer to all the others, and
where one of the candidates within wins, pairwise. Smith is
just mutual dominant set with n->inf.
2. Condorcet for sets. Smith is Condorcet for sets. If a
set can beat all those outside the set pairwise, it should
win. If the set is of size one, well, that's just
Condorcet. The only reason why it should hold for size one,
but not, say, size two, is if some other heuristic (like the
Minmax metric/utility heuristic) is more important. If it
is, see my first paragraph; but if we want this method
primarily because it's Condorcet, or because the
Condorcet idea itself is a good one, then we should be
consistent and take that Condorcet as far as possible.
The mutual majority criterion is related to clones.
But it can also be seen as a criterion that refers
to the majority rule and life after the election.
I mean that some majority group may say after the
election "we want these candidates to win" and it
is difficult to explain that they will not get what
they want since they had conflicting opinions within
that candidate set on which one of them should win.
I'm considering the majority rule interpretation; otherwise, I could
just have gone straight for independence of clones. I defined a mutual
dominant set above, and for small values of n, one could reasonably
expect parties (or those who support them) to wonder, if the method is
Condorcet (thus candidates that pairwise beat others are good
candidates), and supports majority rule (thus mutual majority etc), why
it doesn't elect from the mutual dominant nth set. If you have Smith,
you can ensure that it does, no matter how large n is.
Post by Juho Laatu
"Condorcet for sets" sounds a bit "aesthetics based"
to me since I don't know what practical real life
situation (other than aesthetic observations on the
graph that describes the pairwise preferences) could
be used to justify this criterion. If that set was
one candidate (or a nominated party/grouping) then
the basic Condorcet rule would apply, but if the
Smith set is just a random set of candidates and
there is no single majority group of voters behind
this group opinion then it is harder to find the
rationale. (The set members may not be clones and
there may not be a single set of voters that think
that this set is better than others.)
I suppose this leads back to clone independence, so I won't address it
here, except to say that majority for a set makes sense (Mutual
Majority; at least it does to me), and so should Condorcet for a set.
Post by Juho Laatu
One should also ask if the clone criterion is ideal.
For strategy reasons sufficient independence of
clones may be necessary to make it safe for
parties/wings to nominate more than one candidate
(or to nominate only one).
How about the following situation. Both Democrats
and Republicans have three clone candidates. All
votes are sincere. Both parties have 50% support.
The Democrat candidates have a clear group
preference order. The Republican candidates are
badly looped. Is the fact that electing a
Republican candidate would leave us in a
situation where majority of the voters are
not happy but would like to replace this
candidate with another candidate a sufficient
reason to elect the best Democrat candidate
instead. I.e. should we be fully independent of
clones or should we elect the candidate that
seems to be the best compromise candidate /
most agreeable (=least opposition in any
pairwise comparison)?
Independence of clones make the method resistant to nomination
(dis)incentives. Or rather, robust independence of clones (not just
"remove clones, then run through method"), does. This is useful because
one of the major problems with Plurality is that it has a severe
nomination disincentive; if your candidate is similar to some other
candidate, you'll both lose. It's the other way with Borda.

I don't quite see what you're saying. The Democrat candidates have a
clear group preference order, whereas the Republican candidates are
looped; so something like:

50: D1>D2>D3>R1>R2>R3
16: R1>R2>R3>D1>D2>D3
17: R2>R3>R1>D1>D2>D3
17: R3>R1>R2>D1>D2>D3

A cloneproof method would act as if D* and R* are one candidate (more or
less). It may pick R3 instead of R1 because 18 instead of 16 preferred
that one, but it shouldn't switch from R* to D*.

For the example above, Ranked Pairs / MAM gives the social ordering D1 =
R1 > D2 = R2 > D3 = R3.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
In what situations would the single winner and the social
ordering differ? It does, for proportional completion
(because that's proportional and thus PR-esque thinking
appllies), but to majority methods... I can't quite see
when that would be the case.
No need to be different. I was just thinking
that they may be used for different purposes
and therefore may be different.
Would there be a situation where "first from a social ordering" and
"best single winner" would be different in a single-winner election? If
so, what is that situation? (I assume there's no tie for first place.)
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Now they're not strict clones anymore. A good method
should recover gracefully from this condition, since in real
world elections, it's very unlikely that all voters
would vote the clones exactly in the way to make them
obvious as clones. The prefix wouldn't do that.
Yes, methods should not identify clones strictly
as in the clone definition. The transitions should
typically be smooth.
There are many ways to identify the clones.
Beatpaths is one approach. Another solution
would be e.g. to allow the candidates to
declare themselves as clones.
This could work for a method with a vote-splitting weakness. In that
respect, I suppose it would be similar to fusion parties, or my
"artificial Condorcet party" idea. However, no candidate would want to
declare himself as clone of somebody else in the context of a system
with a teaming-type weakness. Also, I don't quite see the reason to do
this (compensate for clones) explicitly if one can have a method that
does it implicitly.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Post by Juho Laatu
In Condorcet vote management could be the
most probable path leading to "too high
levels" of strategic voting. In large public
elections with independent voters the risks
are at rather low level.
Do you mean the risks from vote management, or
non-vote-management strategy?
I was thinking something like the Australian
situation where voters are used to vote as told
by the parties in the how-to-vote cards. This
makes it possible to apply strategies that would
not be possible with voters that make independent
(heterogeneous) decisions.
Yes. What does the how-to-vote situation in Australia show us? In my
opinion, it shows that the election method should not demand full
ranking, and that in any event, how-to-vote cards should not be made
part of the official process. I'm not sure if they are in Australia, but
above-the-line voting is pretty close.

Even with a method that permits truncation, parties may tell voters how
to vote. This happened in New York when they used STV, and also in
Ireland. Of course, there's a risk that one'll overextend the vote
management and thus lose seats instead of gain them. Something similar
could happen with Condorcet "game of chicken" dynamics regarding burial,
if a sufficiently large group starts burying. We don't have any data on
the likelihood of single-winner "vote management" (party-directed
strategy), though, simply because preferential single-winner methods
haven't been used long enough.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Post by Juho Laatu
A unified front of respected experts could do
a lot. Unfortunately all the experts seem to
have their own favourite methods and
corresponding campaigns :-).
That was a reference to Minmax. If you throw
nonmonotonicity at IRV, they might throw reversal symmetry
failure at you in return.
I wouldn't mind that since I don't see reversal
symmetry as a requirement for group opinions on
single winners. I sort of expect the society to
be mature enough to handle also the tricky
questions in some rational way.
Well, yes, but would the people? Of those that agree that
nonmonotonicity is a problem, would most also consider reversal symmetry
of no great importance? In the worst case, people wouldn't understand
Arrow at all, and the various groups could end up using that to fling
criterion failures at each other.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
As for experts, again we hit the problem of estimating how
much strategy would happen. Ideally, we'd either have
that data or we'd have some way of saying "all we
mean is that Condorcet is good: if you want something good
but possibly complex, choose this, otherwise..", and
unite under Condorcet. Perhaps some sort of "here's
the criteria the different methods pass, pick what you think
would be best", but I think knowing real world strategy
so we could find a single Condorcet method would be better.
I'd appreceate e.g. a web site that would aim at
neutral description of all the relevant methods
(plausible candidates for election reforms), with
estimates on how they would perform in real life.
How would we get those estimates? By testing the methods?
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Juho Laatu
2008-12-06 23:00:48 UTC
Permalink
Post by Kristofer Munsterhjelm
Alright. You may like Minmax for being Minmax, and
that's okay; but in my case, I'm not sure if it
would withstand strategy (there's that "hard to
estimate the amount of strategy that will happen"
again), and the Minmax heuristic itself doesn't seem
important enough to trade things like clone independence and
Smith for.
The good points in Minmax are related to behaviour
with sincere votes. It is not really rigged to
remove maximum number or amount of strategic threats
(but to implement one natural sincere utility
function). The question then is which properties one
should emphasize (electing the right winner vs. not
electing a wrong winner due to strategic voting).

All Condoret methods are vulnerable to some very
basic strategies. Some Condorcet methods try to
fix some additional threats. One may say that
differences in the level of vulnerability are not
that big. And fixing one problem often leads to
vulnerability on some other area.

One may say that all Condorcet methods are quite
resistant to strategic voting, espacially in the
typical environments (large public elections with
independent decision making and with limited
information on how others are going to vote).

I say this to present Minmax in a positive light.
Maybe the fairness of the method is also a
positive value. Maybe the strategic defences are
not needed, especially since there is a risk that
we don't elect the best winner then. Maybe focus
on the positive properties even encourages sincere
voting (=let's just pick the best winner). Maybe
the Minmax viewpoint to who is best is accurate
enough for the purpose.

And if there are meninful strategies and counter
strategies then I think the method may already
have failed.

Minmax is not necessarily the ideal utility
function (for ranked votes). I think different
elections may well have different sincere needs.
Different methods may be used for different needs.
In Minmax it is quite easy to justify electing
Condorcet loser (in some very rare cases) or to
fail strict clone compliancy (in some very rare
cases). Also mutual majority can be explained away
(I already tried this in this mail stream) but
here it is easier to give space also to other
opinions.

Some more words on trading clone independence and
Smith. Note that Minmax doesn't trade them away
since it respects them almost always. (And in these
cases we can diecuss if it is justified to violate
these criteria in these special cases.) A less than
100% compliance with some criteria may sometimes be
useful. Either beneficial or acceptable because some
criteria need to be violated in any case.

I did'n btw quite like term "Minmax heuristic" since
my dictionary defines heuristic in mathematics,
science and philosophy as "using or obtained by
exploration of possibilities rather than by
following set rules". The rules and justifyig
explanations of Minmax(margins) are very exact.
(Actually most other Condorcet methods are more
inclined towards heuristic style exploration, e.g.
to find the most strategy resistant methods.)
Post by Kristofer Munsterhjelm
Post by Juho Laatu
One should also ask if the clone criterion is ideal.
For strategy reasons sufficient independence of
clones may be necessary to make it safe for
parties/wings to nominate more than one candidate
(or to nominate only one).
How about the following situation. Both Democrats
and Republicans have three clone candidates. All
votes are sincere. Both parties have 50% support.
The Democrat candidates have a clear group
preference order. The Republican candidates are
badly looped. Is the fact that electing a
Republican candidate would leave us in a
situation where majority of the voters are
not happy but would like to replace this
candidate with another candidate a sufficient
reason to elect the best Democrat candidate
instead. I.e. should we be fully independent of
clones or should we elect the candidate that
seems to be the best compromise candidate /
most agreeable (=least opposition in any
pairwise comparison)?
Independence of clones make the method resistant to
nomination (dis)incentives. Or rather, robust independence
of clones (not just "remove clones, then run through
method"), does. This is useful because one of the major
problems with Plurality is that it has a severe nomination
disincentive; if your candidate is similar to some other
candidate, you'll both lose. It's the other way with
Borda.
I don't quite see what you're saying. The Democrat
candidates have a clear group preference order, whereas the
50: D1>D2>D3>R1>R2>R3
16: R1>R2>R3>D1>D2>D3
17: R2>R3>R1>D1>D2>D3
17: R3>R1>R2>D1>D2>D3
A cloneproof method would act as if D* and R* are one
candidate (more or less). It may pick R3 instead of R1
because 18 instead of 16 preferred that one, but it
shouldn't switch from R* to D*.
For the example above, Ranked Pairs / MAM gives the social
ordering D1 = R1 > D2 = R2 > D3 = R3.
Yes that's what I thought except that maybe the
Democrats were neutral with respect to the
Republican candidates (D1>D2>D3>R1=R2=R3) or had
similar circular opinions as the Republican voters.

To me the interesting question is which one is
better, D1 or R1. D1 doesn't lose to anyone. R1
would lose (with the modified votes) to R3 quite
badly (i.e. the voters would like to change R1 to
R3 after R1 has been elected).

Should we then not elect the "most satisfying" D1.
Or should we strictly stick to the ideal that if
Republicans had not nominated R3 (that caused the
problems to R1) then R1 would have won (if the
votes had otherwise stayed the same).

Note that this violation of clone independence
may not be a big enough threat to the parties to
discourage nomination of more than one candidate.
I guess it would be more typical that nomination
of more than one candidate increases the
probability of that party to win the election.
(I also note that nomination of two candidates
looks still very safe from this example point
of view :-).)
Post by Kristofer Munsterhjelm
Would there be a situation where "first from a social
ordering" and "best single winner" would be
different in a single-winner election? If so, what is that
situation? (I assume there's no tie for first place.)
No. For one need, to elect a single winner,
picking that single winner from the top of the
social ordering should make no difference. I
expect the society to determine the criteria
well, and that should point out one of the
candidate (or a tie). The tail of the social
ordering is irrelevant (i.e. one could use
different conflicting social orderings to
point out the same single winner).
Post by Kristofer Munsterhjelm
Post by Juho Laatu
There are many ways to identify the clones.
Beatpaths is one approach. Another solution
would be e.g. to allow the candidates to
declare themselves as clones.
This could work for a method with a vote-splitting
weakness. In that respect, I suppose it would be similar to
fusion parties, or my "artificial Condorcet party"
idea. However, no candidate would want to declare himself as
clone of somebody else in the context of a system with a
teaming-type weakness. Also, I don't quite see the
reason to do this (compensate for clones) explicitly if one
can have a method that does it implicitly.
Just one option. Other approaches may not be
perfect / ideal for he need either.
Post by Kristofer Munsterhjelm
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Post by Juho Laatu
In Condorcet vote management could be the
most probable path leading to "too high
levels" of strategic voting. In large
public
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Post by Juho Laatu
elections with independent voters the risks
are at rather low level.
Do you mean the risks from vote management, or
non-vote-management strategy?
I was thinking something like the Australian
situation where voters are used to vote as told
by the parties in the how-to-vote cards. This
makes it possible to apply strategies that would
not be possible with voters that make independent
(heterogeneous) decisions.
Yes. What does the how-to-vote situation in Australia show
us? In my opinion, it shows that the election method should
not demand full ranking, and that in any event, how-to-vote
cards should not be made part of the official process.
I'm not sure if they are in Australia, but
above-the-line voting is pretty close.
Even with a method that permits truncation, parties may
tell voters how to vote. This happened in New York when they
used STV, and also in Ireland. Of course, there's a risk
that one'll overextend the vote management and thus lose
seats instead of gain them. Something similar could happen
with Condorcet "game of chicken" dynamics
regarding burial, if a sufficiently large group starts
burying. We don't have any data on the likelihood of
single-winner "vote management" (party-directed
strategy), though, simply because preferential single-winner
methods haven't been used long enough.
I see Condorcet methods as excellent methods if
the level of strategic voting stays at random
noise level. If majority of the voters start
voting strategically, either in their own style
or (worse) based on centrally coordinated
strategies then I'd be willing to consider
moving to use some other methods with which
this particular society would work better
(maybe down to Plurality and wait for things
to settle). It is however quite probable that
in many societies Condorcet methods would work
fine (including Minmax).
Post by Kristofer Munsterhjelm
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Post by Juho Laatu
A unified front of respected experts could do
a lot. Unfortunately all the experts seem to
have their own favourite methods and
corresponding campaigns :-).
That was a reference to Minmax. If you throw
nonmonotonicity at IRV, they might throw reversal
symmetry
Post by Juho Laatu
Post by Kristofer Munsterhjelm
failure at you in return.
I wouldn't mind that since I don't see
reversal
Post by Juho Laatu
symmetry as a requirement for group opinions on
single winners. I sort of expect the society to
be mature enough to handle also the tricky
questions in some rational way.
Well, yes, but would the people? Of those that agree that
nonmonotonicity is a problem, would most also consider
reversal symmetry of no great importance? In the worst case,
people wouldn't understand Arrow at all, and the various
groups could end up using that to fling criterion failures
at each other.
We have seen that it is easy to generate all
kind of bad examples, violations of nice
looking criteria, biased terminology, and to
ignore some of the weak spot's of one's own
favourite method, and to emphasize different
points in the right way. Election methods are
complex enough and the example cases
interesting enough to do this. For this
reason I mentioned the unified front of
respected experts. Maybe solutions like
Wikipedia would work too, but also there
I see lots of black and white for and
against opinions. Maybe we are also lacking
a scientific method based community of
practical implementation related election
method research with a popularization arm.
Post by Kristofer Munsterhjelm
Post by Juho Laatu
I'd appreceate e.g. a web site that would aim at
neutral description of all the relevant methods
(plausible candidates for election reforms), with
estimates on how they would perform in real life.
How would we get those estimates? By testing the methods?
Since there can be many kind of tests with many
kind of simplification and bias I'd trust also
here a team of trusted experts or a scientific
community with strong emphasis on seeking best
results with respect to practical applicability
of the results in real life.

Tests are often just very basic artifical models
of real life situations. Therefore they need to
be interpreted. And here we may need to trust
the expert group or community to focus on the
relevant aspects.

I btw trust also on simple example cases. They
are useful in demonstrating how probable the
benefits and vulnerablities are in real life.

Juho







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Kristofer Munsterhjelm
2008-12-14 20:27:33 UTC
Permalink
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Alright. You may like Minmax for being Minmax, and
that's okay; but in my case, I'm not sure if it
would withstand strategy (there's that "hard to
estimate the amount of strategy that will happen"
again), and the Minmax heuristic itself doesn't seem
important enough to trade things like clone independence and
Smith for.
The good points in Minmax are related to behaviour
with sincere votes. It is not really rigged to
remove maximum number or amount of strategic threats
(but to implement one natural sincere utility
function). The question then is which properties one
should emphasize (electing the right winner vs. not
electing a wrong winner due to strategic voting).
All Condoret methods are vulnerable to some very
basic strategies. Some Condorcet methods try to
fix some additional threats. One may say that
differences in the level of vulnerability are not
that big. And fixing one problem often leads to
vulnerability on some other area.
There is probably a Pareto front in this respect. Just like some methods
fail more criteria than others, some methods would do both worse on
sincere votes and resist strategy less; it would be Pareto-dominated by
better methods. But since there's a Pareto front and not a single
objective, some methods on that front will be better at translating
sincere expression (whatever metric is used to measure this), while some
are much more resistant against strategy.

If we take that further, some compliances are probably more "expensive"
than others. Intuitively, I think clone independence is pretty
inexpensive (that it alters situations that is much more likely to be
due to strategy than honest voting), but I have no proof of this, of
course; and similarly intuitively, I think that MDQBR (mutual dominant
quarter burial resistance) would be very expensive, since so many voters
are burying that the dishonest ballot bundle will collide with a sincere
ballot bundle (in the latter case, the "buriers' candidate" should win,
because there are no buriers and the expression is sincere).
Post by Juho Laatu
One may say that all Condorcet methods are quite
resistant to strategic voting, espacially in the
typical environments (large public elections with
independent decision making and with limited
information on how others are going to vote).
That's what it all boils down to. We don't know whether Condorcet
methods are adequately resistant. The cover-all-bases approach is to try
to have the method pass as many criteria as possible so that even in the
worst case, the system resists strategy. If the criteria are cheap,
there's little harm (except the waste of work, but having a margin of
safety is probably a good thing, ceteris paribus). The other approach
would be to actually investigate the kind of strategy that would
develop, but this is difficult: even if we had access to near-unlimited
numbers of experiments, we wouldn't know whether the dynamics would lead
to things like vote management on one hand, or the initial strategy
resistance would discourage people from building upon them on the other.
Post by Juho Laatu
I say this to present Minmax in a positive light.
Maybe the fairness of the method is also a
positive value. Maybe the strategic defences are
not needed, especially since there is a risk that
we don't elect the best winner then. Maybe focus
on the positive properties even encourages sincere
voting (=let's just pick the best winner). Maybe
the Minmax viewpoint to who is best is accurate
enough for the purpose.
And if there are meninful strategies and counter
strategies then I think the method may already
have failed.
Minmax is not necessarily the ideal utility
function (for ranked votes). I think different
elections may well have different sincere needs.
Different methods may be used for different needs.
In Minmax it is quite easy to justify electing
Condorcet loser (in some very rare cases) or to
fail strict clone compliancy (in some very rare
cases). Also mutual majority can be explained away
(I already tried this in this mail stream) but
here it is easier to give space also to other
opinions.
This raises the question: for ranked electoral methods, what is the
ideal utility function, or more precisely, what is the ideal honest
aggregation function? One may argue for Borda being it (Bayesian
regret), or Minmax (gives up as little as possible), Kemeny-Young
(maximum likelihood, maximize the number of voters that agree with each
preference) or Dodgson (minimize ballot differences to CW). In the case
of different ideal functions for different needs, the question is
displaced to what conditions would make, say, Minmax, optimal.
Post by Juho Laatu
Some more words on trading clone independence and
Smith. Note that Minmax doesn't trade them away
since it respects them almost always. (And in these
cases we can diecuss if it is justified to violate
these criteria in these special cases.) A less than
100% compliance with some criteria may sometimes be
useful. Either beneficial or acceptable because some
criteria need to be violated in any case.
That goes both ways. If Minmax respects them almost always, then wanting
a method that behaves maximally like Minmax except when doing so would
make it vulnerable to cloning (or non-Smith, or whatever), trades off
little for a large "margin of safety" gain, since the situations are
rare. Of course, the other way is what you mentioned, that if they are
rare situations, then there may not be a point in making the method more
complex just to cover them. (Then again, one should note that in the
face of an adversary, corner cases will occur more often than usual,
since the adversary will actively seek them out if they benefit it.)
Post by Juho Laatu
I did'n btw quite like term "Minmax heuristic" since
my dictionary defines heuristic in mathematics,
science and philosophy as "using or obtained by
exploration of possibilities rather than by
following set rules". The rules and justifyig
explanations of Minmax(margins) are very exact.
(Actually most other Condorcet methods are more
inclined towards heuristic style exploration, e.g.
to find the most strategy resistant methods.)
Granted, though I think most Condorcet methods are rigorous. Schulze (by
the beatpath definition) would give an objective to be maximized by
reasoning that if there's a circular tie, the candidate that indirectly
beats the others is preferrable. At the election methods level,
"programs" and "functions" become very similar, and one may be phrased
in terms of the other, generally speaking; it would be hard to make a
functional description of say, first preference Copeland, or "Condorcet
else IRV".
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Independence of clones make the method resistant to
nomination (dis)incentives. Or rather, robust independence
of clones (not just "remove clones, then run through
method"), does. This is useful because one of the major
problems with Plurality is that it has a severe nomination
disincentive; if your candidate is similar to some other
candidate, you'll both lose. It's the other way with
Borda.
I don't quite see what you're saying. The Democrat
candidates have a clear group preference order, whereas the
50: D1>D2>D3>R1>R2>R3
16: R1>R2>R3>D1>D2>D3
17: R2>R3>R1>D1>D2>D3
17: R3>R1>R2>D1>D2>D3
A cloneproof method would act as if D* and R* are one
candidate (more or less). It may pick R3 instead of R1
because 18 instead of 16 preferred that one, but it
shouldn't switch from R* to D*.
For the example above, Ranked Pairs / MAM gives the social
ordering D1 = R1 > D2 = R2 > D3 = R3.
Yes that's what I thought except that maybe the
Democrats were neutral with respect to the
Republican candidates (D1>D2>D3>R1=R2=R3) or had
similar circular opinions as the Republican voters.
To me the interesting question is which one is
better, D1 or R1. D1 doesn't lose to anyone. R1
would lose (with the modified votes) to R3 quite
badly (i.e. the voters would like to change R1 to
R3 after R1 has been elected).
Should we then not elect the "most satisfying" D1.
Or should we strictly stick to the ideal that if
Republicans had not nominated R3 (that caused the
problems to R1) then R1 would have won (if the
votes had otherwise stayed the same).
Note that this violation of clone independence
may not be a big enough threat to the parties to
discourage nomination of more than one candidate.
I guess it would be more typical that nomination
of more than one candidate increases the
probability of that party to win the election.
(I also note that nomination of two candidates
looks still very safe from this example point
of view :-).)
Even if it had been D1 = R3 > D2 = R2 > D3 = R1, it would still have
been cloneproof. I think I see what you mean, though; in a way, it's
similar to the argument in favor of D'Hondt (as a divisor method among
others) that parties can only gain by joining - there should be a
disincentive to fragmenting.

Obviously, my example is a two-party situation, so yes, there a primary
plus plurality would probably work as well, but it's a contrived example.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Would there be a situation where "first from a social
ordering" and "best single winner" would be
different in a single-winner election? If so, what is that
situation? (I assume there's no tie for first place.)
No. For one need, to elect a single winner,
picking that single winner from the top of the
social ordering should make no difference. I
expect the society to determine the criteria
well, and that should point out one of the
candidate (or a tie). The tail of the social
ordering is irrelevant (i.e. one could use
different conflicting social orderings to
point out the same single winner).
Which means that one may use Kemeny, which outputs a social ordering and
minimizes a measure on potential orderings, to pick a winner (or more
generally, any such method). If the tail of the social ordering doesn't
matter, one can simply remove it afterwards (although I suppose that
could lead to people asking why the metric should be on a social
ordering scale in the first place).
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Even with a method that permits truncation, parties may
tell voters how to vote. This happened in New York when they
used STV, and also in Ireland. Of course, there's a risk
that one'll overextend the vote management and thus lose
seats instead of gain them. Something similar could happen
with Condorcet "game of chicken" dynamics
regarding burial, if a sufficiently large group starts
burying. We don't have any data on the likelihood of
single-winner "vote management" (party-directed
strategy), though, simply because preferential single-winner
methods haven't been used long enough.
I see Condorcet methods as excellent methods if
the level of strategic voting stays at random
noise level. If majority of the voters start
voting strategically, either in their own style
or (worse) based on centrally coordinated
strategies then I'd be willing to consider
moving to use some other methods with which
this particular society would work better
(maybe down to Plurality and wait for things
to settle). It is however quite probable that
in many societies Condorcet methods would work
fine (including Minmax).
I would rather have a Condorcet method on the strategy side of the
Pareto front than plain old Plurality; or if the society's so interested
in strategizing, use DSV Approval and set the human "grandmasters"
against computers. That might be too complex, however, but would be a
fair version of what might happen in any case if the base method allowed
optimization/strategy: various parties would start using computers to
find the ideal strategic vote.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Well, yes, but would the people? Of those that agree that
nonmonotonicity is a problem, would most also consider
reversal symmetry of no great importance? In the worst case,
people wouldn't understand Arrow at all, and the various
groups could end up using that to fling criterion failures
at each other.
We have seen that it is easy to generate all
kind of bad examples, violations of nice
looking criteria, biased terminology, and to
ignore some of the weak spot's of one's own
favourite method, and to emphasize different
points in the right way. Election methods are
complex enough and the example cases
interesting enough to do this. For this
reason I mentioned the unified front of
respected experts. Maybe solutions like
Wikipedia would work too, but also there
I see lots of black and white for and
against opinions. Maybe we are also lacking
a scientific method based community of
practical implementation related election
method research with a popularization arm.
That's a good idea, and I think it would be useful if we were to move to
an advocate stage. Create or find a group that's sufficiently scientific
to understand the question and the methods, yet sufficiently independent
to say "this seems best to me" outside of the context of EM messages.
The other aspect of the method would be simplicity and the relative
importance of criteria (how easy it would be to popularize, and what
obstacles it may face from opponents), and that aspect would be more
readily answered by potential voters (ordinary people), as those are
after all who would be using whatever method one would focus on advocating.
Post by Juho Laatu
Post by Kristofer Munsterhjelm
Post by Juho Laatu
I'd appreceate e.g. a web site that would aim at
neutral description of all the relevant methods
(plausible candidates for election reforms), with
estimates on how they would perform in real life.
How would we get those estimates? By testing the methods?
Since there can be many kind of tests with many
kind of simplification and bias I'd trust also
here a team of trusted experts or a scientific
community with strong emphasis on seeking best
results with respect to practical applicability
of the results in real life.
Tests are often just very basic artifical models
of real life situations. Therefore they need to
be interpreted. And here we may need to trust
the expert group or community to focus on the
relevant aspects.
Yes, though simulations can be contentious. Consider, for instance,
Bayesian regret.
Post by Juho Laatu
I btw trust also on simple example cases. They
are useful in demonstrating how probable the
benefits and vulnerablities are in real life.
Yee diagrams are good here, I think. The situations they model are ones
that could practically happen; it's a lower bound of sorts - if a method
shows odd results there, it would be suspect, but the converse may not
be true.
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Juho Laatu
2008-12-14 22:54:29 UTC
Permalink
Post by Kristofer Munsterhjelm
--- On Fri, 5/12/08, Kristofer Munsterhjelm
Post by Kristofer Munsterhjelm
Alright. You may like Minmax for being Minmax, and
that's okay; but in my case, I'm not sure
if it
Post by Kristofer Munsterhjelm
would withstand strategy (there's that
"hard to
Post by Kristofer Munsterhjelm
estimate the amount of strategy that will
happen"
Post by Kristofer Munsterhjelm
again), and the Minmax heuristic itself
doesn't seem
Post by Kristofer Munsterhjelm
important enough to trade things like clone
independence and
Post by Kristofer Munsterhjelm
Smith for.
The good points in Minmax are related to behaviour
with sincere votes. It is not really rigged to
remove maximum number or amount of strategic threats
(but to implement one natural sincere utility
function). The question then is which properties one
should emphasize (electing the right winner vs. not
electing a wrong winner due to strategic voting).
All Condoret methods are vulnerable to some very
basic strategies. Some Condorcet methods try to
fix some additional threats. One may say that
differences in the level of vulnerability are not
that big. And fixing one problem often leads to
vulnerability on some other area.
There is probably a Pareto front in this respect. Just like
some methods fail more criteria than others, some methods
would do both worse on sincere votes and resist strategy
less; it would be Pareto-dominated by better methods. But
since there's a Pareto front and not a single objective,
some methods on that front will be better at translating
sincere expression (whatever metric is used to measure
this), while some are much more resistant against strategy.
If we take that further, some compliances are probably more
"expensive" than others. Intuitively, I think
clone independence is pretty inexpensive (that it alters
situations that is much more likely to be due to strategy
than honest voting), but I have no proof of this, of course;
and similarly intuitively, I think that MDQBR (mutual
dominant quarter burial resistance) would be very expensive,
since so many voters are burying that the dishonest ballot
bundle will collide with a sincere ballot bundle (in the
latter case, the "buriers' candidate" should
win, because there are no buriers and the expression is
sincere).
Yes. We may complain when the favourite
of the strategists is elected with some
set of votes. But we should also always
ask the question who should have been
elected if we would have a similar set
of sincere votes (or if some other group
of strategists changed the votes in the
reverse direction).
Post by Kristofer Munsterhjelm
One may say that all Condorcet methods are quite
resistant to strategic voting, espacially in the
typical environments (large public elections with
independent decision making and with limited
information on how others are going to vote).
That's what it all boils down to. We don't know
whether Condorcet methods are adequately resistant.
The Condorcet methods have at least
passed one of my tests. I have several
times asked the election method experts
to give a simple set of strategic rules
that voters could apply in Condorcet
elections for their benefit. But I have
not seen any. The next task would be to
point out real life like election
examples where strategies are easy and
riskless enough so that they could be
publicly recommended to voters (in typical
large public elections). Also this has
been quite difficult to achieve. One
could also try to find out strategic
opportunities in coming real life
Condorcet elections and try to find
good strategic advices for voters in
them. I haven't seen this either.
All this does not prove that Condorcet
would not fall in some scenarios, but
at least this shows some direction and
something about the typical behaviour.
(Also methods that are currently widely
used do have vulnerabilities.)
Post by Kristofer Munsterhjelm
The
cover-all-bases approach is to try to have the method pass
as many criteria as possible so that even in the worst case,
the system resists strategy. If the criteria are cheap,
there's little harm (except the waste of work, but
having a margin of safety is probably a good thing, ceteris
paribus). The other approach would be to actually
investigate the kind of strategy that would develop, but
this is difficult: even if we had access to near-unlimited
numbers of experiments, we wouldn't know whether the
dynamics would lead to things like vote management on one
hand, or the initial strategy resistance would discourage
people from building upon them on the other.
Real life testing is probably the best
thing to do.
Post by Kristofer Munsterhjelm
I say this to present Minmax in a positive light.
Maybe the fairness of the method is also a
positive value. Maybe the strategic defences are
not needed, especially since there is a risk that
we don't elect the best winner then. Maybe focus
on the positive properties even encourages sincere
voting (=let's just pick the best winner). Maybe
the Minmax viewpoint to who is best is accurate
enough for the purpose.
And if there are meninful strategies and counter
strategies then I think the method may already
have failed.
Minmax is not necessarily the ideal utility
function (for ranked votes). I think different
elections may well have different sincere needs.
Different methods may be used for different needs.
In Minmax it is quite easy to justify electing
Condorcet loser (in some very rare cases) or to
fail strict clone compliancy (in some very rare
cases). Also mutual majority can be explained away
(I already tried this in this mail stream) but
here it is easier to give space also to other
opinions.
This raises the question: for ranked electoral methods,
what is the ideal utility function, or more precisely, what
is the ideal honest aggregation function? One may argue for
Borda being it (Bayesian regret), or Minmax (gives up as
little as possible), Kemeny-Young (maximum likelihood,
maximize the number of voters that agree with each
preference) or Dodgson (minimize ballot differences to CW).
In the case of different ideal functions for different
needs, the question is displaced to what conditions would
make, say, Minmax, optimal.
Some more words on trading clone independence and
Smith. Note that Minmax doesn't trade them away
since it respects them almost always. (And in these
cases we can diecuss if it is justified to violate
these criteria in these special cases.) A less than
100% compliance with some criteria may sometimes be
useful. Either beneficial or acceptable because some
criteria need to be violated in any case.
That goes both ways. If Minmax respects them almost always,
then wanting a method that behaves maximally like Minmax
except when doing so would make it vulnerable to cloning (or
non-Smith, or whatever), trades off little for a large
"margin of safety" gain, since the situations are
rare. Of course, the other way is what you mentioned, that
if they are rare situations, then there may not be a point
in making the method more complex just to cover them. (Then
again, one should note that in the face of an adversary,
corner cases will occur more often than usual, since the
adversary will actively seek them out if they benefit it.)
I did'n btw quite like term "Minmax
heuristic" since
my dictionary defines heuristic in mathematics,
science and philosophy as "using or obtained by
exploration of possibilities rather than by
following set rules". The rules and justifyig
explanations of Minmax(margins) are very exact.
(Actually most other Condorcet methods are more
inclined towards heuristic style exploration, e.g.
to find the most strategy resistant methods.)
Granted, though I think most Condorcet methods are
rigorous. Schulze (by the beatpath definition) would give an
objective to be maximized by reasoning that if there's a
circular tie, the candidate that indirectly beats the others
is preferrable. At the election methods level,
"programs" and "functions" become very
similar, and one may be phrased in terms of the other,
generally speaking; it would be hard to make a functional
description of say, first preference Copeland, or
"Condorcet else IRV".
Post by Kristofer Munsterhjelm
Independence of clones make the method resistant
to
Post by Kristofer Munsterhjelm
nomination (dis)incentives. Or rather, robust
independence
Post by Kristofer Munsterhjelm
of clones (not just "remove clones, then run
through
Post by Kristofer Munsterhjelm
method"), does. This is useful because one of
the major
Post by Kristofer Munsterhjelm
problems with Plurality is that it has a severe
nomination
Post by Kristofer Munsterhjelm
disincentive; if your candidate is similar to some
other
Post by Kristofer Munsterhjelm
candidate, you'll both lose. It's the
other way with
Post by Kristofer Munsterhjelm
Borda.
I don't quite see what you're saying. The
Democrat
Post by Kristofer Munsterhjelm
candidates have a clear group preference order,
whereas the
Post by Kristofer Munsterhjelm
Republican candidates are looped; so something
50: D1>D2>D3>R1>R2>R3
16: R1>R2>R3>D1>D2>D3
17: R2>R3>R1>D1>D2>D3
17: R3>R1>R2>D1>D2>D3
A cloneproof method would act as if D* and R* are
one
Post by Kristofer Munsterhjelm
candidate (more or less). It may pick R3 instead
of R1
Post by Kristofer Munsterhjelm
because 18 instead of 16 preferred that one, but
it
Post by Kristofer Munsterhjelm
shouldn't switch from R* to D*.
For the example above, Ranked Pairs / MAM gives
the social
Post by Kristofer Munsterhjelm
ordering D1 = R1 > D2 = R2 > D3 = R3.
Yes that's what I thought except that maybe the
Democrats were neutral with respect to the
Republican candidates (D1>D2>D3>R1=R2=R3) or
had
similar circular opinions as the Republican voters.
To me the interesting question is which one is
better, D1 or R1. D1 doesn't lose to anyone. R1
would lose (with the modified votes) to R3 quite
badly (i.e. the voters would like to change R1 to
R3 after R1 has been elected).
Should we then not elect the "most
satisfying" D1.
Or should we strictly stick to the ideal that if
Republicans had not nominated R3 (that caused the
problems to R1) then R1 would have won (if the
votes had otherwise stayed the same).
Note that this violation of clone independence
may not be a big enough threat to the parties to
discourage nomination of more than one candidate.
I guess it would be more typical that nomination
of more than one candidate increases the
probability of that party to win the election.
(I also note that nomination of two candidates
looks still very safe from this example point
of view :-).)
Even if it had been D1 = R3 > D2 = R2 > D3 = R1, it
would still have been cloneproof. I think I see what you
mean, though; in a way, it's similar to the argument in
favor of D'Hondt (as a divisor method among others) that
parties can only gain by joining - there should be a
disincentive to fragmenting.
If there is a target of avoiding
fragmentation that should be clearly
stated. Otherwise that property should
be counted as a flaw.

Same with Condorcet methods. One
should make it clear if the target is
e.g. not to hinder nomination of
multiple candidates per party.

(And one should directly or indirectly
also say if is ok to count losses to
other candidates as "negative points"
also when all those candidates are
(according to some measure) clones of
the candidate in question.)
Post by Kristofer Munsterhjelm
Obviously, my example is a two-party situation, so yes,
there a primary plus plurality would probably work as well,
but it's a contrived example.
Post by Kristofer Munsterhjelm
Would there be a situation where "first from
a social
Post by Kristofer Munsterhjelm
ordering" and "best single winner"
would be
Post by Kristofer Munsterhjelm
different in a single-winner election? If so, what
is that
Post by Kristofer Munsterhjelm
situation? (I assume there's no tie for first
place.)
No. For one need, to elect a single winner,
picking that single winner from the top of the
social ordering should make no difference. I
expect the society to determine the criteria
well, and that should point out one of the
candidate (or a tie). The tail of the social
ordering is irrelevant (i.e. one could use
different conflicting social orderings to
point out the same single winner).
Which means that one may use Kemeny, which outputs a social
ordering and minimizes a measure on potential orderings, to
pick a winner (or more generally, any such method).
Yes, although it might look strange if
changes in the social ordering somewhere
down below would in some cases change
also the most preferred candidate.
Post by Kristofer Munsterhjelm
If the
tail of the social ordering doesn't matter, one can
simply remove it afterwards (although I suppose that could
lead to people asking why the metric should be on a social
ordering scale in the first place).
Post by Kristofer Munsterhjelm
Even with a method that permits truncation,
parties may
Post by Kristofer Munsterhjelm
tell voters how to vote. This happened in New York
when they
Post by Kristofer Munsterhjelm
used STV, and also in Ireland. Of course,
there's a risk
Post by Kristofer Munsterhjelm
that one'll overextend the vote management and
thus lose
Post by Kristofer Munsterhjelm
seats instead of gain them. Something similar
could happen
Post by Kristofer Munsterhjelm
with Condorcet "game of chicken"
dynamics
Post by Kristofer Munsterhjelm
regarding burial, if a sufficiently large group
starts
Post by Kristofer Munsterhjelm
burying. We don't have any data on the
likelihood of
Post by Kristofer Munsterhjelm
single-winner "vote management"
(party-directed
Post by Kristofer Munsterhjelm
strategy), though, simply because preferential
single-winner
Post by Kristofer Munsterhjelm
methods haven't been used long enough.
I see Condorcet methods as excellent methods if
the level of strategic voting stays at random
noise level. If majority of the voters start
voting strategically, either in their own style
or (worse) based on centrally coordinated
strategies then I'd be willing to consider
moving to use some other methods with which
this particular society would work better
(maybe down to Plurality and wait for things
to settle). It is however quite probable that
in many societies Condorcet methods would work
fine (including Minmax).
I would rather have a Condorcet method on the strategy side
of the Pareto front than plain old Plurality; or if the
society's so interested in strategizing, use DSV
Approval and set the human "grandmasters" against
computers. That might be too complex, however, but would be
a fair version of what might happen in any case if the base
method allowed optimization/strategy: various parties would
start using computers to find the ideal strategic vote.
(Note btw that finding the ideal
strategic votes for all the voters
is typically easier than also
implementing that strategy in real
life elections.)
Post by Kristofer Munsterhjelm
Post by Kristofer Munsterhjelm
Well, yes, but would the people? Of those that
agree that
Post by Kristofer Munsterhjelm
nonmonotonicity is a problem, would most also
consider
Post by Kristofer Munsterhjelm
reversal symmetry of no great importance? In the
worst case,
Post by Kristofer Munsterhjelm
people wouldn't understand Arrow at all, and
the various
Post by Kristofer Munsterhjelm
groups could end up using that to fling criterion
failures
Post by Kristofer Munsterhjelm
at each other.
We have seen that it is easy to generate all
kind of bad examples, violations of nice
looking criteria, biased terminology, and to
ignore some of the weak spot's of one's own
favourite method, and to emphasize different
points in the right way. Election methods are
complex enough and the example cases
interesting enough to do this. For this
reason I mentioned the unified front of
respected experts. Maybe solutions like
Wikipedia would work too, but also there
I see lots of black and white for and
against opinions. Maybe we are also lacking
a scientific method based community of
practical implementation related election
method research with a popularization arm.
That's a good idea, and I think it would be useful if
we were to move to an advocate stage. Create or find a group
that's sufficiently scientific to understand the
question and the methods, yet sufficiently independent to
say "this seems best to me" outside of the context
of EM messages. The other aspect of the method would be
simplicity and the relative importance of criteria (how easy
it would be to popularize, and what obstacles it may face
from opponents), and that aspect would be more readily
answered by potential voters (ordinary people), as those are
after all who would be using whatever method one would focus
on advocating.
One basic requirement in a democracy
is also that the (decision making)
citizens do understand how the system
works. They are not cattle but the
ultimate decision makers that need to
understand both the content and the
working methods at some suitable
level. Clear modelling and clear
descriptions are this essential to
make a democracy work better.

This is of course quite important
especially in complex areas like
voting methods and the related
mechanisms and behaviour of democracy
in general. Good modelling and
presentation needed to make any
progress.
Post by Kristofer Munsterhjelm
Post by Kristofer Munsterhjelm
Post by Juho Laatu
I'd appreceate e.g. a web site that would
aim at
Post by Kristofer Munsterhjelm
Post by Juho Laatu
neutral description of all the relevant
methods
Post by Kristofer Munsterhjelm
Post by Juho Laatu
(plausible candidates for election reforms),
with
Post by Kristofer Munsterhjelm
Post by Juho Laatu
estimates on how they would perform in real
life.
Post by Kristofer Munsterhjelm
How would we get those estimates? By testing the
methods?
Since there can be many kind of tests with many
kind of simplification and bias I'd trust also
here a team of trusted experts or a scientific
community with strong emphasis on seeking best
results with respect to practical applicability
of the results in real life.
Tests are often just very basic artifical models
of real life situations. Therefore they need to
be interpreted. And here we may need to trust
the expert group or community to focus on the
relevant aspects.
Yes, though simulations can be contentious. Consider, for
instance, Bayesian regret.
Yes, they all need good interpretation.
I also often think that the society is
in any case a more complex animal than
what the simplifying theories and
models describe. That means that in
order to explain one may need a bit
wider understanding of the environment
than just mechanical understanding of
the used tests and simulations, simplified
criteria, simplified requirements etc.
Definitions, simulations and models can
also be built to present only one
viewpoint to the topic in question.
Post by Kristofer Munsterhjelm
I btw trust also on simple example cases. They
are useful in demonstrating how probable the
benefits and vulnerablities are in real life.
Yee diagrams are good here, I think. The situations they
model are ones that could practically happen; it's a
lower bound of sorts - if a method shows odd results there,
it would be suspect, but the converse may not be true.
Yes, nice pictures that offer good
information on what the utility
function of each method looks like.
Also they (and their limitations)
need to be explained well.

Juho







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Election-Methods mailing list - see http://electorama.com/em for list info
Chris Benham
2008-11-25 06:02:29 UTC
Permalink
Greg,
I've come to the strong view that truncation (e.g. bullet voting)
without order-reversal  shouldn't really qualify as a (insincere)
"strategy".

I don't see any point or use in us trying to distinguish between:
truncation because the voter is sincerely ambivalent or has no
preference among the unranked candidates, truncation because
the voter's preferences among the unranked candidates are too
weak for her to be bothered recording, or truncation because the
voter fears being stung by later-harm or is deliberately concealing
a clear pairwise preference in a diabolical scheme to thwart the
election of a  shining sincere Condorcet winner.

I agree that resistance to Burying is atractive and  IRV's big selling
point versus Condorcet methods. 

Chris Benham


Greg Dennis wrote (Sat.Nov.22):
Perhaps intuitiveness is a bit in the eyes of the beholder, but I'll
tell you the strategies I find intuitive:

- Burying a candidate with strong first choice support
- Bullet voting for a candidate with strong first choice support
- A compromise in which you switch your first choice vote to a
candidate who has stronger first choice support.

-snip-

...I have grown to believe resistance to burying essential.

-snip-


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Kristofer Munsterhjelm
2008-11-25 09:37:48 UTC
Permalink
Post by Chris Benham
Greg,
I've come to the strong view that truncation (e.g. bullet voting)
without order-reversal shouldn't really qualify as a (insincere)
"strategy".
truncation because the voter is sincerely ambivalent or has no
preference among the unranked candidates, truncation because
the voter's preferences among the unranked candidates are too
weak for her to be bothered recording, or truncation because the
voter fears being stung by later-harm or is deliberately concealing
a clear pairwise preference in a diabolical scheme to thwart the
election of a shining sincere Condorcet winner.
I agree that resistance to Burying is atractive and IRV's big selling
point versus Condorcet methods.
As we know, Smith,IRV is resistant to burial (hence my statement of "if
you're going to have IRV, have Smith,IRV", since you gain Condorcet
compliance). I also think Minmax-elimination is resistant to burial (at
least it elects the "right" candidate in your Mutual Dominant Quarter
example).

However, IRV is nonmonotonic. Is it possible to make a monotonic method
that's resistant to burial? Dominant Mutual Third resistance? Dominant
Mutual Quarter? It would give very unintuitive results, but might be
needed if most of the electorate go "on a burial spree". I know of no
method that actually has these properties, though; the method I called
"first preference Copeland" was shown to be nonmonotonic as well
(incidentally, by you:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2007
-January/019135.html )

(FPC is the method that, for each candidate, its penalty is the sum of
the first preference votes of the ones that pairwise beat it. Whoever
has least penalty wins.)

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Juho Laatu
2008-11-25 19:30:40 UTC
Permalink
Post by Chris Benham
I agree that resistance to Burying is atractive and IRV's big selling
point versus Condorcet methods.
Yes, this may be the strongest selling argument of IRV
against Condorcet. But I think this doesn't yet mean
that Condorcet methods would in real life be vulnerable
to burying. Use of burial may require good understanding
of the opinions of others and good coordination, and may
include risks, and requires many voters to accept the
idea of strategic voting. My hope thus is that these
threats would mostly remain theoretical.

Juho








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Chris Benham
2008-11-25 15:21:11 UTC
Permalink
Kristopher,
All Condorcet methods are vulnerable to Burial. Smith,IRV has in
common with IRV but not the other well-known Condorcet methods
that a Mutual Dominant Third winner can't be buried. But like all other
Condorcet methods it is not absolutely invulnerable to Burial like IRV.

37: A>B
31: B>A
32: C>B

B is the CW, but if the A>B voters bury B by changing to A>C then
the Smith,IRV winner changes from B to A.

For the advantage over IRV of the difference between Smith and
Mutual Dominant Third (MDT), we lose Burial Invulnerability and
Later-no-Harm and Later-no-Help and Mono-add-Top.

So I think the argument that Smith,IRV is really much better than the
simpler plain IRV is weak. Likewise the case that Smith,IRV is the
best Condorcet method.

"Is it possible to make a monotonic method  that's resistant to burial?"

Yes, FPP fills that bill. Other methods have  incentives to "bury" only
by truncating, not order-reversing. (According to a definition I'm not
entirely happy with this qualifiies as "burying"). I have in mind the methods
that met Later-no-Help and not Later-no-Harm, such as Bucklin and
Approval.

Chris Benham
 
 
 
 
Kristofer Munsterhjelm  wrote (Tues.Nov.25):
As we know, Smith,IRV is resistant to burial (hence my statement of "if
you're going to have IRV, have Smith,IRV", since you gain Condorcet
compliance). I also think Minmax-elimination is resistant to burial (at
least it elects the "right" candidate in your Mutual Dominant Quarter
example).

However, IRV is nonmonotonic. Is it possible to make a monotonic method
that's resistant to burial? Dominant Mutual Third resistance? Dominant
Mutual Quarter? It would give very unintuitive results, but might be
needed if most of the electorate go "on a burial spree". I know of no
method that actually has these properties, though; the method I called
"first preference Copeland" was shown to be nonmonotonic as well
(incidentally, by you:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2007
-January/019135.html )

(FPC is the method that, for each candidate, its penalty is the sum of
the first preference votes of the ones that pairwise beat it. Whoever
has least penalty wins.)



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Kristofer Munsterhjelm
2008-11-25 17:29:40 UTC
Permalink
Post by Chris Benham
Kristopher,
All Condorcet methods are vulnerable to Burial. Smith,IRV has in
common with IRV but not the other well-known Condorcet methods
that a Mutual Dominant Third winner can't be buried. But like all other
Condorcet methods it is not absolutely invulnerable to Burial like IRV.
37: A>B
31: B>A
32: C>B
B is the CW, but if the A>B voters bury B by changing to A>C then
the Smith,IRV winner changes from B to A.
For the advantage over IRV of the difference between Smith and
Mutual Dominant Third (MDT), we lose Burial Invulnerability and
Later-no-Harm and Later-no-Help and Mono-add-Top.
So I think the argument that Smith,IRV is really much better than the
simpler plain IRV is weak. Likewise the case that Smith,IRV is the
best Condorcet method.
I wouldn't say Smith,IRV is the best Condorcet method, either, but it
may be the closest thing if people are very inclined towards burying
candidates (and we want Condorcet).
Post by Chris Benham
"Is it possible to make a monotonic method that's resistant to burial?"
Yes, FPP fills that bill. Other methods have incentives to "bury" only
by truncating, not order-reversing. (According to a definition I'm not
entirely happy with this qualifiies as "burying"). I have in mind the methods
that met Later-no-Help and not Later-no-Harm, such as Bucklin and
Approval.
It would seem that in order for a method to be completely resistant to
burial (including truncation), it must meet both LNHelp and LNHarm. That
makes sense, because Burial involves altering the position of those
lower down on your ranking to help the candidate that's higher up in
your ranking. However, we know from Woodall that we can't have both
LNHs, mutual majority, and monotonicity, nor can we have LNH* and
Condorcet. Thus a method that's completely resistant would seem to need
to be nonmonotonic or fail mutual majority, and in either case fail
Condorcet.

There is one way out: consider a method that fails LNH* only in such
ways that are not conducive to burial. For instance, it may be that if
you vote A>B>C, then moving B last would cause C to win (instead of B).
This is like Warren's claims about Black (Condorcet else Borda). You
gave an example where burial works in Black, so Black is somewhat
susceptible to burial, but it's theoretically possible there may be a
method that works this way.

There's also another caveat in the other direction: consider a method
with compulsory full ranking and a fixed number of candidates. It may be
susceptible to burial (order reversal) even if LNH* no longer make any
sense.

-

FPTP works, but really just because you can't bury. This can technically
be "fixed" by treating FPTP as a ranked voting method where only your
first preference matters. Still, it's a bit of a trick, so let me try
something a bit more detailed. I wonder if there's a method that meets
Condorcet and Dominant Mutual * burial resistance (the lesser the
fraction the better), and is also monotonic. Both Smith,IRV and "first
preference Copeland" meet Dominant Mutual Third burial resistance, but
they're both nonmonotonic. While I'm wishing, having it summable would
also be nice.

Or, for that matter, do we have a method that meets DMTBR, mutual
majority, and monotonicity? Perhaps DAC (since it meets LNHelp), but it
has other problems, and it doesn't meet plain DMT.
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Markus Schulze
2008-11-28 00:41:00 UTC
Permalink
Hallo,
Post by Juho Laatu
I didn't quite get this. When evaluating
candidate X minmax just checks if voters
would be interested in changing X to some
other candidate (in one step), while
methods like Schulze and Ranked Pairs may
base their evaluation on chains of victories
leading to X.
Suppose the MinMax score of a set Y of candidates
is the strength of the strongest win of
a candidate A outside the set Y against
a candidate B inside the set Y. Then the
Schulze method (but not the Ranked Pairs
method) guarantees that the winner is
always chosen from the set with minimum
MinMax score. See section 9 of my paper:

http://m-schulze.webhop.net/schulze1.pdf

Because of this reason, the worst pairwise
defeat of the Schulze winner is usually very
weak. And, in most cases, the Schulze winner
is identical to the MinMax winner. This has
been confirmed by Norman Petry and Jobst
Heitzig (with different models):

http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html

Markus Schulze


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Juho Laatu
2008-11-28 06:48:44 UTC
Permalink
Thanks, the referred paper contains a clear explanation of the links between minmax and Schulze. Use of the "minmax criterion" (max interest to change to another candidate) for groups too differs from the basic minmax method in that also other pairwise preferences than those that involve candidate X directly may influence the evaluation of candidate X.

My understanding is that the main driver behind the beatpath based methods has been the interest to guarantee independence of clones (well, maybe some aesthetic values too). Unfortunately all the criteria are not compatible with each others, and doing this takes one step away from the "minmax criterion" for individual candidates (that can be used as one possible sincere social utility criterion - at least the margins based version).

Using beatpaths to identify clones is also not an exact definition of which candidates are clones, but at least it covers all clones (when defined as "candidates next to each others in every ballot"). In that sense beatpaths may be seen a slight overkill, but maybe a necessary one (?) if one wants independence of clones and the decisions to be based on the pairwise comparison matrix only.

Juho
Subject: Re: [EM] Why I Prefer IRV to Condorcet
Date: Friday, 28 November, 2008, 2:41 AM
Hallo,
Post by Juho Laatu
I didn't quite get this. When evaluating
candidate X minmax just checks if voters
would be interested in changing X to some
other candidate (in one step), while
methods like Schulze and Ranked Pairs may
base their evaluation on chains of victories
leading to X.
Suppose the MinMax score of a set Y of candidates
is the strength of the strongest win of
a candidate A outside the set Y against
a candidate B inside the set Y. Then the
Schulze method (but not the Ranked Pairs
method) guarantees that the winner is
always chosen from the set with minimum
http://m-schulze.webhop.net/schulze1.pdf
Because of this reason, the worst pairwise
defeat of the Schulze winner is usually very
weak. And, in most cases, the Schulze winner
is identical to the MinMax winner. This has
been confirmed by Norman Petry and Jobst
http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html
Markus Schulze
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Chris Benham
2008-12-10 19:17:21 UTC
Permalink
Kristofer,

You wrote (Sun.Nov.23):
"Regarding number two, simple Condorcet methods exist. Borda-elimination
(Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody
who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll
partially grant this, though, since the good methods are complex, but
I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In
MAM, you take all the pairwise contests, sort by strength, and affirm
down the list unless you would contradict an earlier affirmed contest.
This method is cloneproof, monotonic, etc..."

Raynaud isn't  Borda-elimination.  It is  Pairwise Elimination, i.e. eliminate
the loser of  the most decisive or strongest pairwise result (by one measure or
another) until one candidate remains.  You may have instead meant to write
"Baldwin",though some sources just talk about 2 different versions of  Nanson.

Simpler and much better than any of those methods are  Condorcet//Approval
and  Smith//Approval and  Schwartz//Approval ,in each case interpreting
ranking as approval and so not allowing ranking among unapproved candidates.

Chris Benham


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Kristofer Munsterhjelm
2008-12-11 10:11:26 UTC
Permalink
Post by Chris Benham
Kristofer,
"Regarding number two, simple Condorcet methods exist. Borda-elimination
(Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody
who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll
partially grant this, though, since the good methods are complex, but
I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In
MAM, you take all the pairwise contests, sort by strength, and affirm
down the list unless you would contradict an earlier affirmed contest.
This method is cloneproof, monotonic, etc..."
Raynaud isn't Borda-elimination. It is Pairwise Elimination, i.e.
eliminate the loser of the most decisive or strongest pairwise result
(by one measure or another) until one candidate remains. You may have
instead meant to write "Baldwin",though some sources just talk about
2 different versions of Nanson.
Simpler and much better than any of those methods are Condorcet//Approval
and Smith//Approval and Schwartz//Approval ,in each case interpreting
ranking as approval and so not allowing ranking among unapproved candidates.
I haven't had the time to reply to the longer posts here yet, but of
course, you're right. I meant to say Baldwin, not Raynaud. The
difference between the two is that one eliminates the loser, while the
other eliminates all below average - somewhat like the difference
between Hare and Carey. Nanson's the average, and Baldwin's the
loser-elimination, unless I'm mistaken.

If you don't like approval cutoffs (implicit or explicit; you probably
have no problem with the implicit ones, but I'm using the general "you"
here), perhaps Smith//Range would work (or for that matter, UncAAO with
range as partial approval, though it's not as simple). One of the
problems with Range is that there's a great incentive to equal-rank
(bottom or top). Interpreting the ballot as a ranked ballot to determine
the Smith (or whatever) set, then breaking ties by whoever has the
greatest score, might ameliorate both Range and Condorcet's problems:
you can't bury without decreasing your score for the tiebreak, and you
can't maximize without throwing some discriminatory power (that's useful
for the first stage) away. Though, on the other hand, it might just lead
to ballots like:

X: 100, Y: 99.999, Z: 99.998, W: 0.003, A: 0.002, B: 0.001, C: 0

But if Smith//Approval is good, then that won't be any worse - well, it
might, somewhat, since you can't have "equal scores but different rank"
in this version.

I guess one of the advantages of implicit Smith//A is that you can't
bury disapproved candidates. Smith//Range would lose this advantage.
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