Discussion:
serious strategy problem in Condorcet, but not in IRV?
James Green-Armytage
2003-08-17 21:13:10 UTC
Permalink
Dear election methods fans,

There is a fellow named Burt Monroe who has a theory that he calls "turkey
raising." I have read a sort of paper of his on the subject, called
"Raising Turkeys: An Extension and Devastating Application of
Myerson-Weber Voting Equilibrium." Looking back into the archives, I found
that Kevin brought the paper up in March, but nobody commented on it. I
don't know if it is on the web, but if anyone wants it, I can send it as
an attached pdf file.

I think that the paper overstates its case, and focuses mostly on voting
systems that nobody really pays attention to now, such as Borda, Nanson,
etc. However, I think that the central idea is worth taking quite
seriously.

The idea seems to be that methods that are sensitive to lower preferences
produce strategy incentives which can result in the likely election of a
candidate who has no sincere support at all, that is, who is ranked dead
last in every voter's sincere preferences.

Monroe says that a method which has this effect fails a criteria he has
made up, called NIA, or nonelection of irrelevant alternatives. According
to him, Condorcet methods fail this criteria, as does Borda, Coombs, and
some others, but it is passed by IRV / the alternative vote, approval
voting, plurality, and runoff. He looks at a bunch of different Condorcet
versions, none of which are beatpath or ranked pairs, but one of which is
Simpson, which to my knowledge is the same as minimax aka sequential
dropping aka successive reversal, and which is equivalent to beatpath and
ranked pairs in most simple cases.

My main concern at this point is with Condorcet and IRV. I have taken the
common wisdom that Condorcet is more resistant to strategy manipulation
than IRV, but this idea challenges that notion. I guess that my goal here
is to reaffirm it, or to accept that IRV is more strategy proof. I am
asking for all of your help in finding out which it is.

Without further ado, let me try to get into an example. This illustrates
my interpretation of the implications of the Monroe paper, which is not
necessarily the same as his intention, but which should be close enough
for starters.

Sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B

It is extremely clear here that C seriously does not deserve to win, as he
is ranked last by 90% of the voters. Also, it is clear that A deserves to
win, albeit by a narrow margin.
Now, if the method is Condorcet (minimax, Schwartz / minimax, ranked
pairs, or beatpath), and if everyone voted sincerely, A would win.
However, if the 44 B>A voters strategically vote B>C (offensive order
reversal), a cycle is formed, in which the defeat of B is now the defeat
of least magnitude, and so B wins.

46: A>B
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 90:10

This is already very unfair, and a clear subversion of the democratic
process.
What can the offended A>B voters do about this? Assuming that the other
preferences are constant they have no way of electing A. Their only
option, other than allowing B to steal the victory, is to truncate or
order-reverse themselves, leading to the election of C. For example,

46: A
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 44:10

The B-->C defeat is the defeat of least magnitude, and so C wins.
The only hope of A voters is that their truncation will deter the B voters
from their order reversal.
Thus the A and B voters have entered a game of chicken. A voters swerving
is their voting sincerely and allowing B to win. B voters swerving is
their voting sincerely and allowing A to win. The car crash is the
election of C.
The outcome is unpredictable. It is quite possible that C will be elected,
despite the fact that he so clearly does not deserve to win. This is not a
pleasant scenario at all from the point of view of democracy, utility,
majority rule, public trust in government, etc.


However, let's say that you have the same sincere preference rankings
while using an IRV system.

46: A>B
44: B>A
5: C>A
5: C>B

In this case, there is nothing that the B voters can do to get B elected,
as long as the other votes are constant. If they vote B>C, it doesn't
matter, as C is eliminated first anyway. So, it looks as though IRV is
more strategy resistant in these sorts of situations than Condorcet is,
unless...

The only way I can see IRV producing a similar result in this situation is
if a lot of B voters initiate the chicken game by taking a loss
themselves, by voting a combination of C>B and B>C instead of B>A. For
example,

46: A>B
26: B>C
5: C>A
23: C>B

Now, the winner is C. The A voters cannot do anything to elect A if the
other voters' rankings remain unchanged, so they have to choose between B
and C. As they do prefer B, they may be moved to switch around their own
preferences so that he is elected instead of C. For example,

35: A>B
11: B>A
26: B>C
5: C>A
23: C>B

B wins. If the A voters are cowed into going along with this, then indeed
the B voters' strange strategy will have paid off in spades.
I believe that this sort of possibility did not occur to Monroe, and I
think that it does contradict his point that IRV can *never* produce
voting games that lead to the election of "irrelevant alternatives."

However, I have to admit that the strategy incentive in the IRV scenario
seems significantly less direct, and less obvious. The B voters have to
start by taking a loss, whereas in the Condorcet scenario, the B voters
can snatch the election away from A without losing anything. This is a
serious point to consider.

The likelihood of the different strategies may depend on what sort of
election scenario the system is being applied to.

One possibility is a series of polls leading up to an actual election,
such as a presidential election. (That is, voters can lie about their
sincere preferences in the polls and thus try to manipulate the rankings
of other voters.) If this is the situation, then I believe that the IRV
strategy and the Condorcet strategy would both work, and both result in a
game of chicken, although admittedly the IRV strategy requires more
imaginative and violent manipulation.

Another possibility is that the voters are going into the election
completely blind to the relative support of the three candidates. I am not
quite sure what would happen in this case, although I would tend to
imagine that voters would vote sincerely. For example, a B voter, not
knowing whether a B>C vote would help elect B over A in a cycle, or just
straight-up elect C, should in theory just tend to vote sincerely. Monroe
might disagree with me here, however. Probably, it depends somewhat on the
relative marginal utility, that is their marginal gain of electing B
instead of A, versus their marginal gain of electing A instead of C. If
their perceived marginal utility of B over A is much greater than that of
A over C, they might be more willing to risk an insincere vote for B>C>A.

There are quite a few different possible scenarios between these two
extremes of totally expressive polls and total blindness before the
election. Maybe voters know that C has very little first place support,
and that A and B are very close.

There is a question of whether strategic conspiracies are allowed to take
place. Is it considered politically acceptable for a party to call up all
of its supporters and ask them to vote insincerely? Also, can they do so
without non-party members finding out about it? Are members of one party
able to send messages to the members of the other party, in order to play
mind games with them and influence their votes?

Unfortunately, I think that these questions will have to be dealt with if
Condorcet is to be applied to the level of public elections.


So, that is my concern. Perhaps Monroe's paper is one of the best
arguments I've heard against Condorcet and against IRV. Hence, it is a
crucial point for any IRV-Condorcet debate. I have very little doubt that
Condorcet produces more fair results than IRV when the votes are sincere,
but is it possible that Condorcet has more serious strategy problems than
IRV?
How can Condorcet advocates respond?

First, I would like to know if anyone has a way to blow Monroe's argument
out of the water, beyond my own relatively lukewarm counter.
Second, I would like to know the logic behind the common wisdom that
Condorcet is more strategy resistant than IRV.
Third, I would like to see the worst (and most likely to occur) strategy
flaws of the IRV system. I would like to see if they can truly be said to
be as serious, and as likely to occur as the Condorcet strategy flaws
given here. I am aware of some of them perhaps, but it would be nice to
try and condense the examples in one place.

I hope that we can make some progress in the strategy debate, which is the
real meat of the IRV-Condorcet issue.


Sincerely (no pun intended),
James





P.S. By the way, here is another example similar to the one I used in this
posting, where C is a less wretched loser, but where manipulation is
easier:

Sincere preferences
30: A>B
25: B>A
23: C>A
22: C>B



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Eric Gorr
2003-08-17 22:57:11 UTC
Permalink
Post by James Green-Armytage
The outcome is unpredictable. It is quite possible that C will be elected,
despite the fact that he so clearly does not deserve to win. This is not a
pleasant scenario at all from the point of view of democracy, utility,
majority rule, public trust in government, etc.
Why?

The voters you are describing are no longer interested in democracy,
majority rule, etc.

When there are such blatant, unapologetic attempts to manipulate the
system, no voting system can possibly save them.

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Dave Ketchum
2003-08-18 02:43:34 UTC
Permalink
Post by Eric Gorr
Post by James Green-Armytage
The outcome is unpredictable. It is quite possible that C will be elected,
despite the fact that he so clearly does not deserve to win. This is not a
pleasant scenario at all from the point of view of democracy, utility,
majority rule, public trust in government, etc.
Why?
The voters you are describing are no longer interested in democracy,
majority rule, etc.
When there are such blatant, unapologetic attempts to manipulate the
system, no voting system can possibly save them.
Just looking at the first example:
It starts with 44: B>A - they consider A to be better than C, and A
wins - GREAT!
Then they switch to 44: B>C - they claim to prefer C over A, and C
wins - ALSO GREAT!

What is NOT GREAT is the propaganda claim that it is unfair for the

voting method to honor their votes just because the propagandist asserts

that their claim to prefer C was insincere.
--
***@clarityconnect.com http://www.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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James Green-Armytage
2003-08-18 03:55:22 UTC
Permalink
Dave, you write
Post by Dave Ketchum
It starts with 44: B>A - they consider A to be better than C, and A
wins - GREAT!
Then they switch to 44: B>C - they claim to prefer C over A, and C
wins - ALSO GREAT!
No, when they switch to B>C, B wins, not C, although C might win
eventually if the A voters respond in kind.
Post by Dave Ketchum
What is NOT GREAT is the propaganda claim that it is unfair for the
voting method to honor their votes just because the propagandist asserts
that their claim to prefer C was insincere.
What do you mean, propaganda claim? I'm telling you straight out that
their votes *are* insincere. I gave the sincere preference rankings at the
beginning, and those don't change. They change their votes because it
benefits B, their sincere first choice. I agree that if they were being
sincere there wouldn't be a problem.

These are my imaginary voters, I made them up, and so I will tell you when
they are being sincere or not. : )

James

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Dave Ketchum
2003-08-18 15:47:59 UTC
Permalink
Post by James Green-Armytage
Dave, you write
Post by Dave Ketchum
It starts with 44: B>A - they consider A to be better than C, and A
wins - GREAT!
Then they switch to 44: B>C - they claim to prefer C over A, and C
wins - ALSO GREAT!
No, when they switch to B>C, B wins, not C, although C might win
eventually if the A voters respond in kind.
Redoing my second assertion:
Then they switch to 44: B>C - they claim to dislike A more than C,
and A loses - ALSO GREAT! As a bonus they managed a win for B, but they
would have had no right to complain if they had managed a win for C,
considering their expressed dislike for A (and, what in real life would be
uncertainty as to exact vote counts to expect).
Post by James Green-Armytage
Post by Dave Ketchum
What is NOT GREAT is the propaganda claim that it is unfair for the
voting method to honor their votes just because the propagandist asserts
that their claim to prefer C was insincere.
What do you mean, propaganda claim? I'm telling you straight out that
their votes *are* insincere. I gave the sincere preference rankings at the
beginning, and those don't change. They change their votes because it
benefits B, their sincere first choice. I agree that if they were being
sincere there wouldn't be a problem.
These are my imaginary voters, I made them up, and so I will tell you when
they are being sincere or not. : )
Ok, but if they do this in real voting they are into dangerous gambling,
for they could succeed in what they claim they want.
Post by James Green-Armytage
James
--
***@clarityconnect.com http://www.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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James Green-Armytage
2003-08-18 14:45:43 UTC
Permalink
Dear Eric,
Post by James Green-Armytage
Post by James Green-Armytage
The outcome is unpredictable. It is quite possible that C will be
elected,
Post by James Green-Armytage
despite the fact that he so clearly does not deserve to win. This is not
a
Post by James Green-Armytage
pleasant scenario at all from the point of view of democracy, utility,
majority rule, public trust in government, etc.
Why?
The voters you are describing are no longer interested in democracy,
majority rule, etc.
When there are such blatant, unapologetic attempts to manipulate the
system, no voting system can possibly save them.
I reply:
Maybe so, but I like to take game theory analyses pretty seriously when
designing a political or economic system.
Game theory assumes that the agents involved aren't interested in the
overall fairness of the system as much as they are interested in getting
their way. A good system from a game theory point of view is one in which
agents act according to their own personal desires, potentially desires
which conflict with each other, yet the overall result is desirable for
society as a whole.

Looking at the current state of American politics, I would say that many
of the agents involved, at least on the high government side of the glass,
show a lot more interest for themselves, their party, their class, their
group, etc., then they do for democracy in general. The voters, perhaps,
are perhaps somewhat less self-interested, but not entirely by any means.
For example, the billionaire who stands to gain from a Bush tax cut or
deregulatory law, and on the other hand maybe a teacher who stands to get
a raise or better funding for their school if the other guy wins.
Whatever. Even when there isn't direct self-interest involved, I think
that the animosity between Democrats and Republicans at present is enough
that many of them would be willing to vote strategically to try to bury
the candidate from the other party.

I am told that when STV was used for school board elections in New York,
parties (or in-groups of some sort) would actually come up with some
pretty elaborate strategies to increase their voting power, and then call
up their supporters and tell them to vote a certain, insincere, way.

Perhaps the best thing we could do, if we wanted to use Condorcet on a
public level would be to make sure that conspiring to such violently
strategic voting would be a matter of political shame, or even illegal. I
am not saying that it is necessarily a fatal problem for Condorcet (Monroe
seems to think so, but that is why I say he overstates his case), but I am
saying that it should be looked at carefully.

sincerely,
James



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Eric Gorr
2003-08-18 14:58:57 UTC
Permalink
Post by James Green-Armytage
Perhaps the best thing we could do, if we wanted to use Condorcet on a
public level would be to make sure that conspiring to such violently
strategic voting would be a matter of political shame, or even illegal.
Yes, it seems to me that such things are a clear case of fraud.


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Dave Ketchum
2003-08-18 15:49:49 UTC
Permalink
Post by Eric Gorr
Post by James Green-Armytage
Perhaps the best thing we could do, if we wanted to use Condorcet on a
public level would be to make sure that conspiring to such violently
strategic voting would be a matter of political shame, or even illegal.
Yes, it seems to me that such things are a clear case of fraud.
Shame - fine - and it can be worded to apply only to those who are guilty.

Illegal - tempting, BUT
B's backers can claim a legitimate goal - A is the worst enemy, so
they should do their best to help A lose.
A's backers can claim a similar goal - B and C are equally good/bad,
so they should be neutral as to B vs C.

How do you prove legal guilt without reading minds? Unless you eavesdrop
on their strategy session and hear an admission?
--
***@clarityconnect.com http://www.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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Eric Gorr
2003-08-18 16:21:19 UTC
Permalink
Post by Dave Ketchum
Post by Eric Gorr
Post by James Green-Armytage
Perhaps the best thing we could do, if we wanted to use Condorcet on a
public level would be to make sure that conspiring to such violently
strategic voting would be a matter of political shame, or even illegal.
Yes, it seems to me that such things are a clear case of fraud.
Shame - fine - and it can be worded to apply only to those who are guilty.
Illegal - tempting, BUT
B's backers can claim a legitimate goal - A is the worst enemy, so
they should do their best to help A lose.
A's backers can claim a similar goal - B and C are equally good/bad,
so they should be neutral as to B vs C.
A legitimate goal can never involve the subversion of voting process.
Post by Dave Ketchum
How do you prove legal guilt without reading minds? Unless you eavesdrop
on their strategy session and hear an admission?
By relying on the only thing that has ever mattered - the desire of
people to do the right thing regardless - when it comes to voting,
that would be to provide a sincere vote.

When that desire is gone, the voting system won't matter.

As for proof...as long as you have people who believe the process is
a good one, you will have people who will come forward.
--
== Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 ===
"Therefore the considerations of the intelligent always include both
benefit and harm." - Sun Tzu
== Insults, like violence, are the last refuge of the incompetent... ===
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James Green-Armytage
2003-08-18 16:55:19 UTC
Permalink
Post by Dave Ketchum
Post by Dave Ketchum
B's backers can claim a legitimate goal - A is the worst enemy, so
they should do their best to help A lose.
A's backers can claim a similar goal - B and C are equally
good/bad,
Post by Dave Ketchum
so they should be neutral as to B vs C.
A legitimate goal can never involve the subversion of voting process.
Myself (James):
I agree with Eric here, in that the B voters are doing is definitely
illigitimate and devious, and shouldn't be tolerated, if it is possible to
stop it.
I have to sympathize with the A voters, however, as they are only trying
to defend their rightfully-winning favorite candidate against an unfair
loss. Also, they never order-reverse, but only truncate.
Still, it is a little hard to figure out where to draw the line.

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Dave Ketchum
2003-08-18 17:19:36 UTC
Permalink
Post by Eric Gorr
Post by Dave Ketchum
Post by Eric Gorr
Post by James Green-Armytage
Perhaps the best thing we could do, if we wanted to use Condorcet on a
public level would be to make sure that conspiring to such violently
strategic voting would be a matter of political shame, or even illegal.
Yes, it seems to me that such things are a clear case of fraud.
Shame - fine - and it can be worded to apply only to those who are guilty.
Illegal - tempting, BUT
B's backers can claim a legitimate goal - A is the worst enemy, so
they should do their best to help A lose.
A's backers can claim a similar goal - B and C are equally good/bad,
so they should be neutral as to B vs C.
A legitimate goal can never involve the subversion of voting process.
How did we get into subversion, other than basing this on voting against
their own interests, which was claimed via the label "insincere"?

The goals I state above are legitimate. Look at:
Greens in 2000 WANTED Nader to win, though this occurring was fantasy.
Greens in 2000 WANTED Bush to lose.
With Plurality they could not express both desires.
With ranked ballots they could have voted Nader>Gore>Bush.
Post by Eric Gorr
Post by Dave Ketchum
How do you prove legal guilt without reading minds? Unless you eavesdrop
on their strategy session and hear an admission?
By relying on the only thing that has ever mattered - the desire of
people to do the right thing regardless - when it comes to voting, that
would be to provide a sincere vote.
And there are people who will do the wrong thing and lie about it. Take
this to court and the big result may be headaches.

I like Condorcet because it is better than IRV at honoring what voters say
with their votes. This should be the best route to discouraging insincere
votes.
Post by Eric Gorr
When that desire is gone, the voting system won't matter.
As for proof...as long as you have people who believe the process is a
good one, you will have people who will come forward.
--
***@clarityconnect.com http://www.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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Eric Gorr
2003-08-18 18:50:59 UTC
Permalink
Post by Dave Ketchum
Post by Eric Gorr
Post by Dave Ketchum
Post by Eric Gorr
Post by James Green-Armytage
Perhaps the best thing we could do, if we wanted to use Condorcet on a
public level would be to make sure that conspiring to such violently
strategic voting would be a matter of political shame, or even illegal.
Yes, it seems to me that such things are a clear case of fraud.
Shame - fine - and it can be worded to apply only to those who are guilty.
Illegal - tempting, BUT
B's backers can claim a legitimate goal - A is the worst enemy, so
they should do their best to help A lose.
A's backers can claim a similar goal - B and C are equally good/bad,
so they should be neutral as to B vs C.
A legitimate goal can never involve the subversion of voting process.
How did we get into subversion, other than basing this on voting
against their own interests, which was claimed via the label
"insincere"?
Voting sincerely is always in the interest of an individual. For in a
collection of people, it is the group preference that is important.
If enough individuals are not prepared to accept a legitimate loss,
the voting system will not matter.

Only in those cases of dictatorships, etc. do pure individual
interests become more important.
--
== Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 ===
"Therefore the considerations of the intelligent always include both
benefit and harm." - Sun Tzu
== Insults, like violence, are the last refuge of the incompetent... ===
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James Green-Armytage
2003-08-18 16:33:39 UTC
Permalink
Dave, et al,
Post by Dave Ketchum
Shame - fine - and it can be worded to apply only to those who are guilty.
Illegal - tempting, BUT
B's backers can claim a legitimate goal - A is the worst enemy, so
they should do their best to help A lose.
A's backers can claim a similar goal - B and C are equally good/bad,
so they should be neutral as to B vs C.
How do you prove legal guilt without reading minds? Unless you eavesdrop
on their strategy session and hear an admission?
I reply:
Certainly you can't punish individual voters for voting insincerely. What
you could do is punish anyone, let's say a party official or employee, who
openly reaches out to the supporters of that party and instructs them to
vote insincerely. For something like this to have an impact in a public
election, it would be necessary to reach out to *a lot* of people, so it
wouldn't be too hard to find out about it.

Perhaps it is analogous to the laws against price fixing in capitalism. It
is seriously illegal for someone from one corporation to call up someone
from a rival corporation and bargain on setting a higher price to increase
both of their profits. Even doing so in a private conversation is illegal.
This is not considered an abridgement of free speech, but a necessary law
to keep the capitalist system from falling apart. Perhaps a law against
this sort of voting strategy conspiracy could be justified on similar
grounds.

However, there is still a vague possibility that such politicians will be
able to get the same effect through sheer negative campaigning, candidates
setting up a real enmity against their biggest rival. Organized strategy
aside, it is possible that in a situation where there are two close
opponents, voters will instinctively rank the other candidate dead last,
even if there are other candidates who they actually find more
objectionable. This kind of risky strategy definitely pays off a lot of
the time if the Borda count is being used. Monroe's argument is that it
also pays off sometimes when using Condorcet, too.

So the worry is that it won't take an organized conspiracy to lead to the
"turkey raising" phenomenon Monroe talks about. Indeed, in his paper there
is no mention of conspiracies; actually his logic is based on the same
kind of analysis as the Duverger law, that is, the probability that a
certain kind of vote will affect the outcome of the election, multiplied
by the marginal utility of that effect for the voter.

It is possible to argue that if two rival candidates smash each other to
bits with negative campaigns and the result is that some third guy gets
elected, then the candidates have gotten what they deserve. Hopefully the
voters will pick the most attractive option out of the remaining
candidates.

What is not so easy to argue is that it is okay for one group of voters to
snatch the election away from a sincere Condorcet winner using strategic
voting. Whether it would take an organized conspiracy for this to happen,
or whether it could happen due to one group of voters being just generally
more devious than the other, I don't know.
Post by Dave Ketchum
Ok, but if they do this in real voting they are into dangerous gambling,
for they could succeed in what they claim they want.
I reply:
Yes. Definitely. That is generally what we hope will hold sway if
Condorcet is being used. Surely, if you strategically reverse the order of
your preferences, you are risking that you will help elect a candidate who
you like even less than the one you are trying to thwart.

However, it is not guaranteed that voters will unwilling to take that
risk.

When the A voters truncate in my example, then they are attempting to make
that risk real, the risk of electing C if the B voters don't shape up and
vote sincerely, or at least just truncate themselves. This creates a game
of chicken though, as I said, where risk is balanced against reward, and
the outcome depends not so much on voter preference as it does on how they
perform in the game of chicken, in terms of their temperament, their
strategy etc.

By the way, as far as the idea of throwing the steering wheel out the
window to win a game of chicken, perhaps the best strategy by members of
one party would be to all cast absentee ballots a certain way (as early as
possible), inform the members of the other party you have done so, and
force them to choose between submission and electing the car crash
candidate.

James




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James Green-Armytage
2003-08-18 17:48:16 UTC
Permalink
Paul writes,
As soon as you get into "what the voters are doing... shouldn't be
tolerated" you are arguing for a dictatorship approach.
It is not what the voters are doing that shouldn't be tolerated. What
shouldn't be tolerated is an attempt by party organizers to advocate an
insincere vote for strategic purposes. That is, telling a voter "vote
A>C>B whether you like C more than B or not, because our polls indicate
that it could create a Condorcet cycle which our man would win," etc.
Allowing people to coordinate their intentions like that is dangerous in
some of the same ways that price fixing is dangerous.
If someone tells her to vote A>B>C and she decides to do so because she
trusts that person's opinion, there is no fault to be found with anyone.
I reply,

I disagree, because the consequences of this, as in my example, are dire.

James

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James Green-Armytage
2003-08-18 19:35:56 UTC
Permalink
Dear election methods fans,

I have noticed one small bright point in this situation which I overlooked
before. Let's think of this as a voting game with multiple rounds, or
perhaps a series of polls leading up to an actual election.

Round one / sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B

A wins. B voters have incentive for offensive order reversal.

46: A>B
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 90:10

B wins.

Here is what I neglected before: At this stage, the 5 C>A voters have an
incentive to change their preferences to A>C, resulting in the election of
A, because they favor A over B.

46: A>B
5: A>C
44: B>C
5: C>B

A:B = 51:49
A:C = 51:49
B:C = 90:10

At this point neither the B>A voters nor the C>B voters (nor of course the
C>A voters) can do anything to get additional gain. So the voting game has
reached a sort of equilibrium, with A, the sincere Condorcet winner, as
the actual winner, cheerfully enough.

Of course, a real situation would not be so tidy and deterministic.
For example, if this was a series of polls leading up to an election.
Sure, the C>A voters switching to A>C would settle the matter. But there
is a possibility that they might prefer to hold on and see what happens
with the chicken game between A>B and B>A voters, hoping that neither will
swerve and C will end up with the victory after all. Another gamble
between risk and reward.

Anyway, this represents a slight improvement for my fairly grim example,
but I will say that the basic problem is still there, and still fairly
unsettling.

James




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Eric Gorr
2003-08-18 21:44:54 UTC
Permalink
Post by James Green-Armytage
Anyway, this represents a slight improvement for my fairly grim example,
but I will say that the basic problem is still there, and still fairly
unsettling.
I still don't understand why it would be so unsettling from the
aspect of an election method.

Considering that all elections methods can be manipulated in some
form or another, what good is it to remind us that society can break
down and make the election method irrelevant by subverting the
process?
--
== Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 ===
"Therefore the considerations of the intelligent always include both
benefit and harm." - Sun Tzu
== Insults, like violence, are the last refuge of the incompetent... ===
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James Green-Armytage
2003-08-19 01:27:14 UTC
Permalink
Dear Eric, et al
Post by Eric Gorr
Voting sincerely is always in the interest of an individual. For in a
collection of people, it is the group preference that is important.
If enough individuals are not prepared to accept a legitimate loss,
the voting system will not matter.
Only in those cases of dictatorships, etc. do pure individual
interests become more important.
I don't think that I agree with this. For one thing, there is the
possibility than an individual actually does have a very clear personal
interest in the election of a particular candidate. Or that they perceive
themselves to have such an interest.
Another possibility is that they are so sure that they are right about
what is good for society, and the supporters of the other candidate are
dead wrong, that they will decide that the ends justify the means, and use
offensive strategy.
Post by Eric Gorr
I still don't understand why it would be so unsettling from the
aspect of an election method.
Considering that all elections methods can be manipulated in some
form or another, what good is it to remind us that society can break
down and make the election method irrelevant by subverting the
process?
Well, I find that fairly disturbing in itself, of course. But perhaps what
worries me about this particular type of scenario is that IRV turns out to
be less manipulable that Condorcet.
Post by Eric Gorr
Of course such flaws should not be ignored, but the flaw that James
was pointing out actually lies utterly outside the scope of an
election method and inside of the scope of what it means to be a
moral/ethical participant in an election.
This is not a dichotomy that voting systems designers have the luxury of
making. If you put in place a system that works great as long as people
vote sincerely, and it works worse in practice than another system that
doesn't produce as-good results given sincere votes, then the people who
implemented the voting system are partly to blame for their lack of
foresight.

Take cardinal ratings, for example. It would be a pretty decent voting
method if you could expect people to vote sincerely in any meaningful way,
but that is just not realistic. A rational voter will tend to give any
given candidate either the highest or the lowest possible score to
maximize their voting power, and so the end result is supposed to be
roughly equivalent to approval.

I'm not saying that approval is so bad, but the point is that any serious
voting system theory (for public elections, at least) expects voters to
try to maximize their voting power, and hence vote strategically. Voting
systems are designed around the principle that they should produce good
results if used this way.

The process of American government now is hardly characterized by very
scrupulous people who refuse to unfairly take advantage of loopholes in
the system. There is no reason to expect that it would suddenly become so
under Condorcet. (I usually think about American government when I think
of government, because I have lived in America all my life. I imagine that
this applies to most governments, but I'm not as qualified to say.) A good
system is one that would minimize the ability of the raging self-interest
of politicians and power groups to subvert the democratic process to the
point of useless absurdity.
Post by Eric Gorr
This is fundamentally different from a flaw one can find within
IRV...where even if one assumes people are perfect and have strictly
voted their sincere preferences, IRV can select an obviously the
wrong winner.
I agree with this. I trust Condorcet to pick a fair winner when people
vote sincerely, but I do not trust IRV to do so.

James



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Eric Gorr
2003-08-19 03:23:20 UTC
Permalink
Post by James Green-Armytage
Dear Eric, et al
Post by Eric Gorr
Voting sincerely is always in the interest of an individual. For in a
collection of people, it is the group preference that is important.
If enough individuals are not prepared to accept a legitimate loss,
the voting system will not matter.
Only in those cases of dictatorships, etc. do pure individual
interests become more important.
I don't think that I agree with this. For one thing, there is the
possibility than an individual actually does have a very clear personal
interest in the election of a particular candidate. Or that they perceive
themselves to have such an interest.
Another possibility is that they are so sure that they are right about
what is good for society, and the supporters of the other candidate are
dead wrong, that they will decide that the ends justify the means, and use
offensive strategy.
Or, in other words, they wish to appoint themselves dictator and
decide the election for themselves. I think you have argued my point
for me.
Post by James Green-Armytage
Post by Eric Gorr
I still don't understand why it would be so unsettling from the
aspect of an election method.
Considering that all elections methods can be manipulated in some
form or another, what good is it to remind us that society can break
down and make the election method irrelevant by subverting the
process?
Well, I find that fairly disturbing in itself, of course. But perhaps what
worries me about this particular type of scenario is that IRV turns out to
be less manipulable that Condorcet.
and IRV is more manipulable in other scenarios...

What is the fundamental aspect in common with all these
scenarios...they each assume enough voters are no longer be
interested in finding the legitimate winner and that they now have
the power to select anyone. When that happens, the election method
becomes quite irrelevant.

Of course, I have to mention again with respect to IRV, that even
when you have a perfect election with people expressing only sincere
preferences, IRV can select an obviously wrong winner.
Post by James Green-Armytage
Post by Eric Gorr
Of course such flaws should not be ignored, but the flaw that James
was pointing out actually lies utterly outside the scope of an
election method and inside of the scope of what it means to be a
moral/ethical participant in an election.
This is not a dichotomy that voting systems designers have the luxury of
making. If you put in place a system that works great as long as people
vote sincerely, and it works worse in practice than another system that
doesn't produce as-good results given sincere votes, then the people who
implemented the voting system are partly to blame for their lack of
foresight.
I believe it to be impossible to design a voting system devoid of all
possible manipulation. When manipulation becomes the sole desire for
a sufficient number of people, it will happen regardless of how
strategy-proof it is.

I also believe that among the most important questions a designer can
ask is would the method, given a perfect election, select an
obviously wrong winner.
Post by James Green-Armytage
Take cardinal ratings, for example. It would be a pretty decent voting
method if you could expect people to vote sincerely in any meaningful way,
but that is just not realistic. A rational voter will tend to give any
given candidate either the highest or the lowest possible score to
maximize their voting power, and so the end result is supposed to be
roughly equivalent to approval.
Well, it would appear to me that Cardinal Ratings fail because it
merely adds undo complication one what would simply turn out to be
either an approval ballot or a ranked ballot.

But, I note that you have stated that rational people would vote
sincerely and in a meaningful way...at least as meaningful as the
Approval method allows.
Post by James Green-Armytage
I'm not saying that approval is so bad, but the point is that any serious
voting system theory (for public elections, at least) expects voters to
try to maximize their voting power, and hence vote strategically. Voting
systems are designed around the principle that they should produce good
results if used this way.
Again, I believe it to be impossible to design a voting system devoid
of all possible manipulation. When manipulation becomes the sole
desire for a sufficient number of people, it will happen regardless
of how strategy-proof it is...

...and manipulation will always be possible, regardless of legality.
Post by James Green-Armytage
The process of American government now is hardly characterized by very
scrupulous people who refuse to unfairly take advantage of loopholes in
the system. There is no reason to expect that it would suddenly become so
under Condorcet.
Of course not, however, under a ranked method, there would at least
be the option again for people to express sincere opinions.

At the moment, the election method is part of the problem because
there simply are more then two choices in the vast majority of
elections.
--
== Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 ===
"Therefore the considerations of the intelligent always include both
benefit and harm." - Sun Tzu
== Insults, like violence, are the last refuge of the incompetent... ===
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Forest Simmons
2003-08-19 18:25:47 UTC
Permalink
Take cardinal ratings, for example ...
A better example would be Borda. It works great, if the voters vote
sincerely and if the parties don't abuse it by running lots of clones.

Forest



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Eric Gorr
2003-08-19 18:38:33 UTC
Permalink
Post by Forest Simmons
Take cardinal ratings, for example ...
A better example would be Borda. It works great, if the voters vote
sincerely and if the parties don't abuse it by running lots of clones.
No, I really don't think Borda does work great as it can obviously
fail even in the case where people are behaving well.

It is quite possible for someone to simply want to run, who is a
clone, and then harm Borda's ability to select the correct winner.


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Forest Simmons
2003-08-19 19:42:01 UTC
Permalink
Post by James Green-Armytage
The process of American government now is hardly characterized by very
scrupulous people who refuse to unfairly take advantage of loopholes in
the system. There is no reason to expect that it would suddenly become so
under Condorcet. (I usually think about American government when I think
of government, because I have lived in America all my life. I imagine that
this applies to most governments, but I'm not as qualified to say.) A good
system is one that would minimize the ability of the raging self-interest
of politicians and power groups to subvert the democratic process to the
point of useless absurdity.
This is an excellent point, along with many others that I have found
illuminating in this thread.

I would like to point out that it is better to say "USA" or "U.S." when
referring to the U.S. since many other countries in the north and south
American continents consider themselves to be "American."

When I was in Argentina, and was asked where I was from, at first I said
that I was from America.

"Norte-america or sudamerica?"

If north, then Mexico, Canada, or USA?

South of the border USA is pronounced "ooh suh" which has the same vowel
sounds as the word tuba.

Forest

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James Green-Armytage
2003-08-18 20:59:09 UTC
Permalink
Dear election methods fans,

I have noticed one small bright point in this situation which I overlooked
before. Let's think of this as a voting game with multiple rounds, or
perhaps a series of polls leading up to an actual election.

Round one / sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B

A wins. B voters have incentive for offensive order reversal.

46: A>B
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 90:10

B wins.

Here is what I neglected before: At this stage, the 5 C>A voters have an
incentive to change their preferences to A>C, resulting in the election of
A, because they favor A over B.

46: A>B
5: A>C
44: B>C
5: C>B

A:B = 51:49
A:C = 51:49
B:C = 90:10

At this point neither the B>A voters nor the C>B voters (nor of course the
C>A voters) can do anything to get additional gain. So the voting game has
reached a sort of equilibrium, with A, the sincere Condorcet winner, as
the actual winner, cheerfully enough.

Of course, a real situation would not be so tidy and deterministic.
For example, if this was a series of polls leading up to an election.
Sure, the C>A voters switching to A>C would settle the matter. But there
is a possibility that they might prefer to hold on and see what happens
with the chicken game between A>B and B>A voters, hoping that neither will
swerve and C will end up with the victory after all. Another gamble
between risk and reward.

Anyway, this represents a slight improvement for my fairly grim example,
but I will say that the basic problem is still there, and still fairly
unsettling.

James




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D***@aol.com
2003-08-18 23:04:26 UTC
Permalink
Eric Gorr wrote in part:

"Considering that all elections methods can be manipulated in some
form or another, what good is it to remind us that society can break
down and make the election method irrelevant by subverting the
process?"

I (quite surprisingly) find myself agreeing with the first half of this
sentence. All election methods are vulnerable to manipulation. However we shouldn't
just sweep any system's flaws under the carpet and pretend they don't exist.
Eric I'm sure wouldn't allow IRV's "flaws" to be swept under the carpet and
ignored.

My personal experience of attempting to defeat Britain's former Conservative
government by encouraging tactical voting ( in order to defeat the
Conservative you vote for the candidate best placed to defeat him/her) is that a large
minority of people have a strong desire to vote sincerely and under plurality
will vote for a candidate they know has little chance of victory and thereby
allow the election of a candidate they don't particularly like as a result.

In real elections the kind of tactics James G-A is describing are unlikely
(IMHO) to happen on a significant enough scale to effect the results. There are
( in my minority opinion) other more serious problems with Condorcet.

One final thought, if a flaw exists in an electoral system I do not consider
it illegitimate to exploit that flaw. If you really want an effective way to
prevent the manipulation of elections you could do what they do in France where
the publication of opinion polls is banned in the two weeks? ( I'm not
certain of the actual time period) before an election.

David Gamble
James Green-Armytage
2003-08-18 23:22:00 UTC
Permalink
However we shouldn't just sweep any system's flaws under the carpet and
pretend they don't exist.
I agree; I think we should take them seriously and try to find the best
way to minimize or correct them. If they are serious enough and can't be
corrected, then it is practical to abandon the system altogether. This is
clearly the last thing I want to do in the case of Condorcet, but is
important to accept evidence against a conclusion that one already feels
strongly about.
In real elections the kind of tactics James G-A is describing are
unlikely (IMHO) to happen on a significant enough scale to effect the
results.
I hope you are right.
One final thought, if a flaw exists in an electoral system I do not
consider it illegitimate to exploit that flaw. If you really want an
effective way to prevent the manipulation of elections you could do what
they do in France where the publication of opinion polls is banned in the
two weeks? ( I'm not certain of the actual time period) before an
election.
So, if there was a law against political organizers directing people to
vote insincerely, would you also consider this to be an effective way to
prevent manipulation?


James

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Eric Gorr
2003-08-18 23:18:05 UTC
Permalink
Post by D***@aol.com
Post by Eric Gorr
Considering that all elections methods can be manipulated in some
form or another, what good is it to remind us that society can break
down and make the election method irrelevant by subverting the
process?
I (quite surprisingly) find myself agreeing with the first half of
this sentence. All election methods are vulnerable to manipulation.
However we shouldn't just sweep any system's flaws under the carpet
and pretend they don't exist. Eric I'm sure wouldn't allow IRV's
"flaws" to be swept under the carpet and ignored.
Of course such flaws should not be ignored, but the flaw that James
was pointing out actually lies utterly outside the scope of an
election method and inside of the scope of what it means to be a
moral/ethical participant in an election.

This is fundamentally different from a flaw one can find within
IRV...where even if one assumes people are perfect and have strictly
voted their sincere preferences, IRV can select an obviously the
wrong winner.


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D***@aol.com
2003-08-18 23:57:56 UTC
Permalink
James

I think a ban on publishing opinion polls in the run up to elections (
freedom of information legislation allowing) would be a lot easier to enforce than a
ban on political organisers directing people how to vote. How would you prove
this or define 'a political organiser' ?

Dvaid Gamble
Markus Schulze
2003-08-19 00:36:09 UTC
Permalink
Dear James Green-Armytage,
Post by James Green-Armytage
Without further ado, let me try to get into an example. This illustrates
my interpretation of the implications of the Monroe paper, which is not
necessarily the same as his intention, but which should be close enough
for starters.
Sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B
It is extremely clear here that C seriously does not deserve to win, as he
is ranked last by 90% of the voters. Also, it is clear that A deserves to
win, albeit by a narrow margin.
Now, if the method is Condorcet (minimax, Schwartz / minimax, ranked
pairs, or beatpath), and if everyone voted sincerely, A would win.
However, if the 44 B>A voters strategically vote B>C (offensive order
reversal), a cycle is formed, in which the defeat of B is now the defeat
of least magnitude, and so B wins.
46: A>B
44: B>C
5: C>A
5: C>B
A:B = 51:49
A:C = 46:54
B:C = 90:10
This is already very unfair, and a clear subversion of the democratic
process.
According to Blake Cretney's terminology, the 44 BAC voters are "burying"
(i.e. ranking a candidate insincerely lower to make him lose). IRV isn't
vulnerable to burying while most other methods are. Therefore, I consider
Monroe's criticism feasible.

Blake Cretney's terminology:
http://www.condorcet.org/emr/defn.shtml

******
Post by James Green-Armytage
I would like to know if anyone has a way to blow Monroe's argument
out of the water, beyond my own relatively lukewarm counter.
I would point to the fact that IRV is vulnerable to "pushing over"
(i.e. ranking a weak candidate higher than one's preferred candidate)
while those methods that meet monotonicity aren't.

******
Post by James Green-Armytage
P.S. By the way, here is another example similar to the one I used in
this posting, where C is a less wretched loser, but where manipulation
Sincere preferences
30: A>B
25: B>A
23: C>A
22: C>B
When IRV is being used, then I suggest that the 25 BAC voters should use
bullet voting so that the 30 ABC voters would have to give their first
preferences to candidate B to keep candidate C from winning.

******
Post by James Green-Armytage
Certainly you can't punish individual voters for voting insincerely. What
you could do is punish anyone, let's say a party official or employee, who
openly reaches out to the supporters of that party and instructs them to
vote insincerely. For something like this to have an impact in a public
election, it would be necessary to reach out to *a lot* of people, so it
wouldn't be too hard to find out about it.
That reminds me of Australia. Here, it wasn't allowed to _ask_ the voters
to use bullet voting. But it was allowed to _educate_ the voters about the
possible consequences of truncated ballots.

Similarily, even when the parties in the USA weren't allowed to _instruct_
their supporters to vote in a certain manner, it wouldn't be possible to
forbid these parties to _educate_ their supporters about the consequences
of voting in a certain manner.

Markus Schulze
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James Green-Armytage
2003-08-19 01:31:41 UTC
Permalink
Dear Markus,
Thank you very much for your input. A couple replies / questions...
Post by Markus Schulze
Post by James Green-Armytage
Sincere preferences
30: A>B
25: B>A
23: C>A
22: C>B
When IRV is being used, then I suggest that the 25 BAC voters should use
bullet voting so that the 30 ABC voters would have to give their first
preferences to candidate B to keep candidate C from winning.
Yes, I agree that the BAC voters have this option. It is similar to the
strategy that the B voters use in my first IRV example. Repeating that for
the sake of clarity:

46: A>B
26: B>C
5: C>A
23: C>B

C wins, and the A voters have to choose between voting for B first or
letting C win.
As I said, the example you have used is easier to manipulate, so the
strategy under IRV that you suggest is much more plausible than the one I
suggest in this example directly above.

I agree that this is a serious problem for IRV as well as for Condorcet,
as both lead to a game of chicken. The IRV strategy, however, is still
slightly less likely than the Condorcet strategy, because the B voters
have to begin the chicken game by taking a loss, whereas in the Condorcet
equivalent, the B voters immediately move to a more desired outcome due to
their strategy.

Thus, the viability of the strategy under IRV depends on B voters
effectively playing psychological games against the A voters, whereas the
strategy under Condorcet can be accomplished by sheer stealth, and in fact
works better if the A voters don't see it coming.
Post by Markus Schulze
I would point to the fact that IRV is vulnerable to "pushing over"
(i.e. ranking a weak candidate higher than one's preferred candidate)
while those methods that meet monotonicity aren't.
Do you mean something like this: (IRV is the method being used)

Sincere preferences
47: Bush
6: Gore > Bush
21: Gore > Nader
26: Nader > Gore

Gore wins IRV.

Strategically altered preferences (2 Bush voters switch to Nader > Bush)

45: Bush
6: Gore > Bush
21: Gore > Nader
26: Nader > Gore
2: Nader > Bush

Gore is eliminated first, and Bush wins. Is this a good example of pushing
over? Certainly the result is pretty screwy, but I'm not quite sure if the
opportunity to use it will come up as often as the opportunity for the
kind of offensive order reversal / burying in my initial example. What do
you think?
Post by Markus Schulze
Similarily, even when the parties in the USA weren't allowed to _instruct_
their supporters to vote in a certain manner, it wouldn't be possible to
forbid these parties to _educate_ their supporters about the consequences
of voting in a certain manner.
Hmm, okay, well, what would you suggest should be used to keep this sort
of strategy in check if Condorcet was ever to be used in serious public
elections where a lot is at stake?




my best,
James










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Markus Schulze
2003-08-19 11:28:48 UTC
Permalink
Dear James Green-Armytage,
Post by Markus Schulze
I would point to the fact that IRV is vulnerable to "pushing over"
(i.e. ranking a weak candidate higher than one's preferred candidate)
while those methods that meet monotonicity aren't.
Do you mean something like this: (IRV is the method being used)
Sincere preferences
47: Bush
6: Gore > Bush
21: Gore > Nader
26: Nader > Gore
Gore wins IRV.
Strategically altered preferences (2 Bush voters switch to Nader > Bush)
45: Bush
6: Gore > Bush
21: Gore > Nader
26: Nader > Gore
2: Nader > Bush
Gore is eliminated first, and Bush wins. Is this a good example of
pushing over?
Yes! But it would have been better if you had used symbols instead
of names. Now, many readers will reply that your example is quite
unrealistic since it is quite improbable that Nader gets 26% of the
first preferences.

******
Post by Markus Schulze
Could it be possible to design a version of Condorcet that is more
strategy-proof than beatpath or ranked pairs?
That depends on what you mean with "strategy-proofness". For example:
Mike Ossipoff and Russ Paielli consider invulnerability to "compromising"
(i.e. ranking a candidate insincerely higher to make him win) to be not
a strategical problem. Therefore, they consider FPP to be strategy-proof.
The only reason why they reject FPP is that FPP can find an "obviously
wrong winner".
Post by Markus Schulze
Plurality is also "extremely difficult to manipulate" in this way,
isn't it? What kind of "offensive strategy" could you possibly use
in plurality? None that I can think of.
(...)
The one and only possible way of helping the Libertarian (or any other
candidate) win is to vote for him. But then you are voting sincerely,
hence you are not "manipulating" anything. Plurality is therefore
beyond manipulation.
What I wanted to say is: From a given point of view, it is rather
subjective which strategical problem (e.g. truncating, burying,
compromising, pushing over) is more offensive, more undesirable,
more drastic, more implausible, more counter-intuitive, etc..

Markus Schulze
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Stephane Rouillon
2003-08-19 15:40:09 UTC
Permalink
Plurality is really easy to manipulate:

suppose sincere preferences
42: A>B>C
44: B>A>C
14: C>A>B

If I am a C>A>B supporter and I have an exact knowledge of the situation,
Instead of voting for C, I would vote for A to make him win instead of
B. Reversely, if I do not have enough information, I could make A win instead
of C.

This is a clear strategy problem. I do not understand how you can say FPTP is
strategy proof. And I particularly find Mr. Monroe design of a class of
strategy
problems that FPTP passes useless when it does not pass other classes.

All electoral systems have strategy-issues (Arrow's theorem), to compare the
different systems,
you would need a measure of the probability strategy cases rising and a
measure
of the gravity of their consequences. Sum up all that you could obtain a mean
deviation per election in term of the number of ranks stolen by the winner
(for single-winner
systems). Calculus are complex because you have to take in account the impact
of
the number of candidates, the number of voters, the real distribution of
preferences,
and finally, definitively not the least, the fraction of each block of voters
(with the same
preferences) that believe a particular scenario will occur.

To get back to my example, B will win unless more than 13 % of the C>A>B
voters
believes that C has no chance winning and decide to act on it.

As long as an electoral method issue can be modified by believes, it is not
strategy-proof.
You only need to make voters believe "your" way.

Hence the best test I can actually think of to asses an election-method
quality is the following:
Suppose a majority of voters wanting a specific candidate.
How many of those voters do you have to make believe something false (about
initial
sincere preferences) to finally steal the election.

Still, it leads to gigantic combinatorial problems and we should take in
account how much
false is a pairwise comparison reversal compared to a bullet ballot change...
However limit cases study could indicate some ranking of electoral methods
"unstrategizable"
levels...

Steph, please comment...
Post by Markus Schulze
Dear James Green-Armytage,
<snip>
Post by Markus Schulze
******
Post by Markus Schulze
Could it be possible to design a version of Condorcet that is more
strategy-proof than beatpath or ranked pairs?
Mike Ossipoff and Russ Paielli consider invulnerability to "compromising"
(i.e. ranking a candidate insincerely higher to make him win) to be not
a strategical problem. Therefore, they consider FPP to be strategy-proof.
The only reason why they reject FPP is that FPP can find an "obviously
wrong winner".
Post by Markus Schulze
Plurality is also "extremely difficult to manipulate" in this way,
isn't it? What kind of "offensive strategy" could you possibly use
in plurality? None that I can think of.
(...)
The one and only possible way of helping the Libertarian (or any other
candidate) win is to vote for him. But then you are voting sincerely,
hence you are not "manipulating" anything. Plurality is therefore
beyond manipulation.
What I wanted to say is: From a given point of view, it is rather
subjective which strategical problem (e.g. truncating, burying,
compromising, pushing over) is more offensive, more undesirable,
more drastic, more implausible, more counter-intuitive, etc..
Markus Schulze
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James Green-Armytage
2003-08-19 16:31:13 UTC
Permalink
James,
your own example
Sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B
shows a typical FPTP informational strategy opportunity.
You should inform Mr. Monroe about it...
It comes from the fact that FPTP forces C>B voters to choose
between C>A=B or A>C=B (using universal ballots syntax).
You cannot assume the degree of information voters have to make their
decision,
it is a part of the strategical problems. Mr. Monroe sets this aside when
he makes his
analysis...
Stephane,

Please keep in mind that I am not really presenting Monroe's argument, but
rather a somewhat bastardized interpretation thereof. However, Monroe
isn't saying that IRV and plurality don't present strategy incentives. I
think that that is obviously wrong. (Also, I doubt that Mike Ossipoff and
Russ Paielli would have made such a statement, because on their web site
they show plurality as failing numerous strategy criteria.) It is a
particular kind of strategy that Monroe is concerned with, and one which
he finds more disturbing than the kind of strategy you illustrate above.

The problem with plurality (and to a lesser extent, with IRV, though not
in this example) is that the C voters are forced to choose between a
sincere vote and the lesser of two evils. In the terminology stated by
Markus in a recent posting, this is the "compromising" strategy.

I agree that it is a very serious problem to force voters to make this
kind of compromising choices on a regular basis, as plurality clearly
does. But what Monroe is concerned with is more so the "burying" strategy,
and its possible consequences. In this particular example, what would
worry him (I think) is that A and B voters will both try to get a bury
each other, and will inadvertently elect C as a result, which I agree
would be a public disaster.

James


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Eric Gorr
2003-08-19 16:50:24 UTC
Permalink
Post by James Green-Armytage
I agree that it is a very serious problem to force voters to make this
kind of compromising choices on a regular basis, as plurality clearly
does. But what Monroe is concerned with is more so the "burying" strategy,
and its possible consequences. In this particular example, what would
worry him (I think) is that A and B voters will both try to get a bury
each other, and will inadvertently elect C as a result, which I agree
would be a public disaster.
But, would this really be *the* disaster or just another symptom of
something that has already gone horribly wrong?

Still seems to me that it can only be a just another symptom of
something that has already gone horribly wrong - as the vast majority
no longer have an interest in finding the legitimate winner, but are
now only interested in finding how they can manipulate the voting
method to cause their candidate to win.

However, the sole reason for hope is that these manipulations can far
to easily backfire causing either the most hated candidate to win
(i.e. C in the case described) or your primary opponent (A or B) to
win.

There has been some concern about polls...however, it seems to me
this concern has been exaggerated. Why? Well, what would become a
natural part of such manipulations would be not providing accurate
information to the poll takers either...manipulating the polls would
simply be part one of manipulating the voting method.

The only way to be certain is with near-perfect information on how
people will vote and obtaining such information is darn near
impossible and would almost certainly involve criminal activity.

The only rational choice a rational voter can therefore make is to
put into place a method which can find the correct winner, based on
sincere votes, and to vote sincerely.
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James Green-Armytage
2003-08-19 17:46:17 UTC
Permalink
Post by James Green-Armytage
In this particular example, what would
Post by James Green-Armytage
worry him (I think) is that A and B voters will both try to get a bury
each other, and will inadvertently elect C as a result, which I agree
would be a public disaster.
But, would this really be *the* disaster or just another symptom of
something that has already gone horribly wrong?
Reading this made me think that if Condorcet was implemented on a big
scale, and a situation like this arose in which the C candidate did
actually win, and a bunch of people blamed Condorcet, I think that it
might be justified for advocates of the system to say "it's not
Condorcet's fault, it's all of your fault for using such a violent and
risky strategy, you dummies."

The A voters might answer, "hey, its not our fault, we were just trying to
defend the rightful winner by deterring the B voters from their violent
strategy." I guess you could pin the blame on any voters who went in for
offensive order-reversal / burying, though (the B voters in my example)...

James

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Craig Carey
2003-08-19 19:12:12 UTC
Permalink
Post by Eric Gorr
Post by James Green-Armytage
I agree that it is a very serious problem to force voters to make this
kind of compromising choices on a regular basis, as plurality clearly
does. But what M[...] is concerned with is more so the "burying" strategy,
...
Post by Eric Gorr
The only rational choice a rational voter can therefore make is to
put into place a method which can find the correct winner, based on
sincere votes, and to vote sincerely.
That is expansive:

* Mr Gorr writes on the correct winner. Please inform about the axioms
that make a 3 candidate 2 winner be perfect.

* Sincerity does not exist. I ask you to post up for me any data you
have on the sincerity numbers for a real election, e.g. an election
between "procedure eg()" subroutines in a multitasking voting
computer program. Obviously I am asking about nothing important if
asking about real elections.

* When replying to my e-mail here, please keep your insincerity (or
lack of earnestness) about your own topic of sincerity well under a
10**(-200) level and

* A sincere method is something that competent theorist neither seek
nor require but instead get, due to how the idea correlates with
axioms that would be used. If you had of written down your axioms
instead of explaining that it is now or never for real voters
(without an ultimatum be provided) then it may have been that an
axiom prevented the problem that you tried to suggest existed.

* However anybody who writes about certifying preferential methods by
writing 100% Ossipoffisms, is probably a EM members who is takes pride
in the joy of sending worthless ideas to the Election Methods List.

* A rational voter could easily stop at rejecting your ideas that are
based upon a presumption that badness is the effect of not removing
their privacy rights. They could be lined up and persusaded to start
conceding that you were in fact correct in making their their
rational reasonings so crucial that is missing entirely from the
paragraph. Mike was doing research into these sorts of areas but
then he said he stopped doing research into voting.

* An optimal method is easily a method you would pronounce to be
unacceptably insincere. The papers can be improved. Why did you not
say how the ballot papers would be redesigned.

How you say that voters must vote sincerely. That means that no 3
vote election in a house, between a boy and 2 puppy dogs, can ever
use a good method your might like by 2006, if the some serious
development demonstrating insincerity occurs during the testing occurs
if your text and the future clarifications are followed.

* Can you give a date at which the sincerity of IRV will present itself
to your mind?. Or is it that you are leading a large breakaway
here at EM into the new social science of assessing the rationality
of random number subroutines and so on.

* The agency calling for the vote is the agency that owns the voice of
all the ballot papers. Two other things are: (1) matters about
the voters (if any), and (2) the counts and preference lists. Your
ideas are clearly having the agency running the vote be out of the
Gorr-voters circle where sincerity is considered in such great
detail that rationality numbers can be computed for each individual.

Where are the sincerity numbers ?. It might look this

(A: 3.0, B: 2.0, C: -0.2, ...)*10**30.


The physical units can be the number of brain cells they have implementing
their own rationality divided by Mr Gorr's in the topic of preferential
voting. Since voting is a topic where the principles are partially quite
easy.

---

Eric is running a coverup over the fact that there is no sincerity
equation. Having such an axiom can be wrong, so there must be a EM-based
need for a coverup on why all other axioms are not there for us to read.
If they are there then a quick check would be done too see if they keep
the power inside the range, 0 to 1, since (unpexectedly) Mr Gorr hints
it might be better to get the winner right.

If Eric wants something then that can be made an axiom. For example, there
could be a set of axioms requiring that no more than 5% of the voters lose
their previously held influence when a preference for a complete loser is
inserted before the winner(s) that would change into a winner and thereby
raise that percentage statistic.

If voters would get rational then maybe they would be perceived by you
to be know what equation provides the sincerity is seemingly wanted by
you. If you ask them and then e-mail the equation out to me, it really
would not help for there is still the whole topic of the consistency of
your axioms. E.g. your hope of sincerity may contradict monotonicity.




Craig Carey
Single Transferable Vote: http://groups.yahoo.com/group/single-transferable-vote

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Forest Simmons
2003-08-21 00:57:42 UTC
Permalink
Post by Eric Gorr
The only rational choice a rational voter can therefore make is to
put into place a method which can find the correct winner, based on
sincere votes, and to vote sincerely.
This idea is interesting to think about:

Suppose for a minute that there is a "correct winner" for each election,
and that you have a method M1 that picks the correct winner when the
voters vote sincerely, but doesn't always do so when the voters use their
optimal strategies.

Suppose also that there is another method M2 that picks the correct winner
in both cases, sincere and strategic.

Since M1 and M2 have no way of knowing if the ballots are sincere or not,
they both pick the winner on the assumption that the ballots are sincere,
and since they both give the same answer (the correct answer) for sincere
ballots, they must agree.

M1 and M2 cannot really give different results in the two cases after all.

This leaves us with four possibilities:

(1) A method that always picks the correct winner with sincere ballots,
also always picks the correct winner when optimal strategies are used by
the voters.

(2) Every method that always picks the correct winner with sincere ballots
fails to pick the correct winner in some cases of strategic ballots.

(3) There is no such thing as a method that always picks the correct
winner for sincere ballots.

(4) "Correct winner" is too fuzzy of a concept to be of much use.


I think we can rule out (1), and that the remaining possibilities are in
order of increasing likelihood.

Here's the most interesting question for me:

Is it possible that increasing resistance to manipulation requires a
sacrifice in the performance of the method in the zero information case?

In other words, manipulation resistance requires a thick skin that puts a
limit on the possible sensitivity and responsiveness of the method to
sincere ballots.

I'm not sure, but I wouldn't be surprised if there were some tradeoff like
this ... a kind of uncertainty principle.

If so, Eric's suggestion above would be one of the two extremes. At the
other extreme we might try to find a method completely resistant to
strategic manipulation and hope that it doesn't work too badly in the zero
info case.

I think that if you had to pick one extreme over the other, I would take
Eric's. But perhaps there is a compromise method that is robust enough to
eliminate most of the manipulation and still do pretty good in the zero
information case.

Recently I have suggested some methods that separate the strategic and
sincere parts of the ballots. The strategic part openly invites strategy
for picking a finalist pair. The sincere part (having nothing to do with
the choice of the finalist pair) elicits the sincere preferences of the
voters to determine which of the two finalists will win the election.

Voters without the interest or patience for participation in the strategic
part can refrain from marking that part without spoiling their ballots.

The strategic part can be any election method applied to pairs of
candidates, i.e. the alternatives to choose from in the strategic part are
pairs of the candidates who are running (individually) in the actual
election.

If the strategic part uses a method that satisfies the weak Favorite
Betrayal Criterion, then the method as a whole satisfies the strong FBC;
since the sincere part of the ballot is not merely expressive; every
sincere preference has some chance of being pivotal.

Any other thoughts along these lines?

Forest

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Alex Small
2003-08-21 03:05:26 UTC
Permalink
Post by Forest Simmons
Suppose for a minute that there is a "correct winner" for each election,
and that you have a method M1 that picks the correct winner when the
voters vote sincerely, but doesn't always do so when the voters use
their optimal strategies.
Suppose also that there is another method M2 that picks the correct
winner in both cases, sincere and strategic.
If you mean the outcome is the same whether people use their optimum
strategies, then it means that there is no incentive to vote insincerely.
If the method uses ranked ballots then it violates the
Gibbard-Satterthwaite Theorem.
Post by Forest Simmons
(4) "Correct winner" is too fuzzy of a concept to be of much use.
Is it possible that increasing resistance to manipulation requires a
sacrifice in the performance of the method in the zero information case?
In other words, manipulation resistance requires a thick skin that puts
a limit on the possible sensitivity and responsiveness of the method to
sincere ballots.
Well, if it isn't responsive to changes in the electorate, then it isn't
very responsive to the ballots received, be their sincere or insincere.

If we think of an election method as partitioning the space of all
possible electorates into distinct regions corresponding to different
winners, then we might measure manipulability by looking at the shape of
boundaries between regions. The more the boundary bends and curves, the
more chances for manipulation. So maybe some sort of geometric or
topological measure of "flatness" or whatever would be useful for
quantifying manipulability.

If we impose the neutrality condition, which is basically a symmetry
condition in the space of all possible electorates, and the anonymity
condition (to reduce the dimensionality of the space from some huge number
depending on the number of voters to some small number depending on the
number of candidates) and the Pareto condition (as a boundary condition)
we could perhaps search for methods that minimize the manipulability.

I'm pretty sure that most proofs of the Gibbard-Satterthwaite Theorem
would show that to minimize manipulability you must elect the Condorcet
Winner when such a candidate exists.




Alex


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Forest Simmons
2003-10-02 01:33:35 UTC
Permalink
Post by Alex Small
Post by Forest Simmons
Is it possible that increasing resistance to manipulation requires a
sacrifice in the performance of the method in the zero information case?
In other words, manipulation resistance requires a thick skin that puts
a limit on the possible sensitivity and responsiveness of the method to
sincere ballots.
Well, if it isn't responsive to changes in the electorate, then it isn't
very responsive to the ballots received, be their sincere or insincere.
Here I was thinking in terms of signal filters. High pass filters are
more responsive to the signal than low pass filters, but also let more
noise through.

Election methods are like filters. The inputs are ballots that reflect
the "noise" that the voters are exposed to as well as the signal, the
truth that they are able to partially discern (mixed in with all of the
noise).

A simpler example is measuring the length of a board. Each voter casts a
vote which is his measurement of the length. An average, median, mode,
midrange, or some other compromise value is taken as the best estimate of
the true length.

Suppose that the length of the board is slowly changing. As new
measurements come in, they can be averaged with recent estimates by a
digital filter y[n+1]=alpha*y[n]+beta*x[n+1] , where alpha+beta=1.

If alpha is large compared to beta, the filter is low pass. It responds
slowly to changes in the length of the board, but it filters out the
measurement errors well.

If alpha is small compared to beta, the filter has greater responsiveness,
but allows measurement errors to have greater influence, as well.

In the context of elections, the electorate changes gradually with the
times. Approval voters, at least, use previous election experience to
help them judge where to put their cutoffs, especially if there are no
reliable comprehensive polls.

It seems to me that there is a trade off in responsiveness and noise
filtering capability in election methods analogous to the same kind of
tradeoff in signal filters.

Forest

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Stephane Rouillon
2003-08-19 19:20:21 UTC
Permalink
I understand but why burial strategy would be more damageable that
any defensive strategy ?
because it can lead to your disastrous C elected result ?
When you do such a behavioral study, you need to take in account human
behavior. Information about vote distribution is biased. Some persons do not
even know what they will vote for yet. In real life you would encounter every
cases: A>C>B, A=B>C, A>B?C so identifying all voters of the same opinion
would be very hard. Even harder to regroup them or communicate which every
one.
And I do not speak about convincing them of the presicion of
your polls and the effect of your collective strategy... Finally, a lot of
people just
want to vote to express their will and they do not care about losing!

So I think electoral models using bullet votes are very more subject to
manipulation,
than Approval, and a lot more than ranking methods...

IMHO, FPTP allows manipulation attempts by one voter with a higher probability
of success
than other methods.

Steph
Post by James Green-Armytage
James,
your own example
Sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B
shows a typical FPTP informational strategy opportunity.
You should inform Mr. Monroe about it...
It comes from the fact that FPTP forces C>B voters to choose
between C>A=B or A>C=B (using universal ballots syntax).
You cannot assume the degree of information voters have to make their
decision,
it is a part of the strategical problems. Mr. Monroe sets this aside when
he makes his
analysis...
Stephane,
Please keep in mind that I am not really presenting Monroe's argument, but
rather a somewhat bastardized interpretation thereof. However, Monroe
isn't saying that IRV and plurality don't present strategy incentives. I
think that that is obviously wrong. (Also, I doubt that Mike Ossipoff and
Russ Paielli would have made such a statement, because on their web site
they show plurality as failing numerous strategy criteria.) It is a
particular kind of strategy that Monroe is concerned with, and one which
he finds more disturbing than the kind of strategy you illustrate above.
The problem with plurality (and to a lesser extent, with IRV, though not
in this example) is that the C voters are forced to choose between a
sincere vote and the lesser of two evils. In the terminology stated by
Markus in a recent posting, this is the "compromising" strategy.
I agree that it is a very serious problem to force voters to make this
kind of compromising choices on a regular basis, as plurality clearly
does. But what Monroe is concerned with is more so the "burying" strategy,
and its possible consequences. In this particular example, what would
worry him (I think) is that A and B voters will both try to get a bury
each other, and will inadvertently elect C as a result, which I agree
would be a public disaster.
James
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Dave Ketchum
2003-08-19 20:15:50 UTC
Permalink
Post by James Green-Armytage
James,
your own example
Sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B
The problem with plurality (and to a lesser extent, with IRV, though not
in this example) is that the C voters are forced to choose between a
sincere vote and the lesser of two evils. In the terminology stated by
Markus in a recent posting, this is the "compromising" strategy.
I agree that it is a very serious problem to force voters to make this
kind of compromising choices on a regular basis, as plurality clearly
does. But what Monroe is concerned with is more so the "burying" strategy,
and its possible consequences. In this particular example, what would
worry him (I think) is that A and B voters will both try to get a bury
each other, and will inadvertently elect C as a result, which I agree
would be a public disaster.
James
Perhaps too many things are getting labeled simply "strategy", defined as
an undesirable activity. Perhaps it can be divided into "normal strategy"
and "devious strategy":

Normal strategy:
In Plurality this is about all I see. Looking above, A and B
backers need not think beyond voting their preference. C backers get to
choose among what I see as sincere votes (or imitations that outsiders
cannot distinguish) (agreed that this makes Plurality an undesirable method):
Vote C to demonstrate backing and express neutrality as to A vs
B or
Vote A or B to help their preference between these win.

In Ranked Balloting the above shows A and B competing in the same
area, thus backing each other as second choice. C backers can both
express C as first choice and their preference among A and B as second choice.

Devious strategy (trying to accomplish your desires by voting something else):
In Plurality I see nothing. A and B backers cannot do better than
their own candidates. C backers are simply expressing their strongest desire.

In Ranked Balloting:
I read above of "burying" - ranking a competitor at the bottom
of the pack, BUT:
If the competitor is that undesirable, this is normal voting.
If this causes a less desirable competitor to win, this
was self destructive deviousness, visiting deserved pain on those so dumb.

In IRV there are many examples of undesirable results, tending to
depend on vote patterns hard to duplicate for devious purposes in real
elections.

In Condorcet another example shows B backers switching from B>A to
B>C and causing B to win. Agreed this is devious, but it depends on exact
vote patterns (beyond what can be planned in normal real elections). A
voters can extend this by bullet voting (saying they do not care between B
and C). Agreed this is devious, but the A voters are accomplishing
exactly what they claimed to want (if they are unable to win, they choose
to leave the decision to B and C voters - who are saying C is acceptable).

In Approval borderline candidates force a difficult decision:
Rank them as if being as desirable as those you like best -
perhaps causing them to win over those you like better.
Rank them as if being as UNdesirable as those you like least -
perhaps causing them to lose to one you like less.

An example I used last month, designed to show difference between IRV and
Post by James Green-Armytage
40 A
30 C>B
30 B
A - odds are against this, and leaves us a tie problem.
IRV - C becomes loser.
Condorcet - B>A and B>C.
IRV - B loses; C loses; A wins; GREAT unhappiness among B backers.
Condorcet - a cycle, B>A and A>C and C>B, but B>A is stronger
than C>B, so B backers are pleased.
Room for IRV deviousness here - getting any voter to convert to C>B lets A win.
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Stephane Rouillon
2003-08-19 20:58:36 UTC
Permalink
Post by Stephane Rouillon
<snip>
I read above of "burying" - ranking a competitor at the bottom
If the competitor is that undesirable, this is normal voting.
If this causes a less desirable competitor to win, this
was self destructive deviousness, visiting deserved pain on those so dumb.
This can happen with plurality too in a three runners election...
Expected:
A: 34
B: 33
C: 32
D: 1
Reality:
A: 33
B: 30
C: 34
D: 1

Supposes I am a C>B>A fan.
If with a friend, we move our vote from C to B to block the expected election of A,

we could end up making A win!!!
Expected after "strategy":
A: 34
B: 35
C: 30
D: 1
Unexpected reality:
A: 33
B: 32
C: 32
D: 1

Classify strategies as much as you want, it is not their nature that is important.
It is their probability of occurence and their consequences.

Steph
Post by Stephane Rouillon
<snip>
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Dave Ketchum
2003-08-20 02:01:18 UTC
Permalink
Post by Stephane Rouillon
Post by Stephane Rouillon
<snip>
I read above of "burying" - ranking a competitor at the bottom
If the competitor is that undesirable, this is normal voting.
If this causes a less desirable competitor to win, this
was self destructive deviousness, visiting deserved pain on those so dumb.
This can happen with plurality too in a three runners election...
A: 34
B: 33
C: 32
D: 1
A: 33
B: 30
C: 34
D: 1
Supposes I am a C>B>A fan.
If with a friend, we move our vote from C to B to block the expected election of A,
we could end up making A win!!!
A: 34
B: 35
C: 30
D: 1
A: 33
B: 32
C: 32
D: 1
Classify strategies as much as you want, it is not their nature that is important.
It is their probability of occurence and their consequences.
Steph
Ok:

You wanted C to win.
You decided that was not possible.
So you made sure C lost.
Deserved - and says deviousness can afflict Plurality, when I thought not.
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Stephane Rouillon
2003-08-20 01:18:21 UTC
Permalink
In a message dated 8/19/03 4:06:08 PM Central Daylight Time,
Post by Stephane Rouillon
This can happen with plurality too in a three runners election...
A: 34
B: 33
C: 32
D: 1
A: 33
B: 30
C: 34
D: 1
Supposes I am a C>B>A fan.
If with a friend, we move our vote from C to B to block the expected
election of A,
we could end up making A win!!!
A: 34
B: 35
C: 30
D: 1
A: 33
B: 32
C: 32
D: 1
Classify strategies as much as you want, it is not their nature that
is important.
It is their probability of occurence and their consequences.
Ok, for us logicians let's try to sort this out.
All the example says to me is that 2 people who voted insincerely
based upon an inaccurate assumption caused their candidate to lose
instead of win.
Markus thinks they are sincere, just compromising. He says it is not
manipulation.
I think they are sincere, but still trying to manipulate the outcome.
Sincere manipulation is still manipulation to me.
That is not a fault of the METHOD, is it? Seems to me that this only
says the 2 voters made a mistake.
Paul Kislanko
I would not say it is the fault of the method.
Those people made the fault by their own decision.
But if a method could avoid people making that fault, would not it be a
BETTER method?
Actually, I think no method is strategy-proof. But some have less
probability of being
manipulated and less consequences to manipulation. Thus it gets us back
to the esperance
measure to compare methods, except we still have problems with the
combinatorial obstacle.

Finally, strategy is not only a probabilistic aspect, it includes
feeding false information to
your adversaries in order to affect their voters behavior. I know I
sound like playing a wargame, but we analyse electoral method using game
theory, don't we?
So if you still think that the previous voters were not manipulating the
electoral system by
getting the most of their ballot, do you agree that their could be
manipulated voters?
If there are methods that prevent manipulation of and by voters, I think
those
are BETTER methods.
That's an argument near what Mike Ossipoff was arguing when defending
winning votes over margins and relative margins... Do not let the system
give the opportunity
to voters to try to improve their result with modified votes based on
the expected ballot
distribution. Wether the manipulation is defined as sincere or unsincere
is not really
relevant to me...

Steph
PS: I hope you do not see anything wrong sharing this with the list...
Markus Schulze
2003-08-20 08:22:36 UTC
Permalink
Dear Stephane,
Post by Stephane Rouillon
Markus thinks they are sincere, just compromising.
He says it is not manipulation.
Russ Paielli thinks they are sincere, just compromising.
He says it is not manipulation.
Markus Schulze
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