Discussion:
Condorcet/Range DSV
Jameson Quinn
2009-06-25 17:55:48 UTC
Permalink
I believe that using Range ballots, renormalized on the Smith set as a
Condorcet tiebreaker, is a very good system by many criteria. I'm of course
not<http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-January/014469.html>the
first one to propose this method, but I'd like to justify and analyze
it
further.

I call the
system Condorcet/Range DSV because it can be conceived as a kind of
Declared Strategy Voting
system, which rationally strategizes voters' ballots for them assuming that
they have correct but not-quite-complete information about all other voters.
Let me explain.

I have been looking into fully-rational DSV methods using Range ballots both
as input and as the underlying method in which strategies play out. It turns
out to be impossible, as far as I can tell, to get a stable, deterministic,
rational result from strategy when there is no Condorcet winner. (Assume
there's a stable result, A. Since A is not a cond. winner, there is some B
which beats A by a majority. If all B>A voters bullet vote for B then B is a
Condorcet winner, and so wins. Thus there exists an offensive strategy. This
proof is not fully general because it neglects defensive strategies, but in
practice trying to work out a coherent, stable DSV which includes defensive
strategies seems impossible to me.) Note that, on the other hand, there MUST
exist a stable probabilistic result, that is, a Nash equilibrium.

Let's take the case of a 3-candidate Smith set to start with. (This
simplifies things drastically and I've never seen a real-world example of a
larger set.) In the Nash equilibrium, all three candidates have a nonzero
probability of winning (or at least, are within one vote of having such a
probability). Voters are dissuaded from using offensive strategy by the real
probability that it would backfire and result in a worse candidate winning.
This Nash equilibrium is in some sense the "best" result, in that all voters
have equal power and no voter can strategically alter it. However, it is
both complicated-to-compute and unnecessarily probabilistic. Forest Simmons has
proposed an interesting
method<http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011028.html>for
artificially reducing the win probability of the less-likely
candidates,
but this method increases computational complexity without being able to
reach a single, fully stable result. (Simmons proposed simply selecting the
most-probable candidate, which is probably the best answer, but it does
invalidate the whole strategic motivation).
There's an easier way. Simply assume that any given voter has only
near-perfect information, not perfect information. That is, each voter knows
exactly which candidates are in the Smith set, but makes an ideosyncratic
(random) evaluation of the probability of each of those candidates winning.
That voter's ideal strategic ballot is an approval style ballot in which all
candidates above their expected value are rated at the top and all
candidates below at the bottom. However, averaging over the different
ballots they'd give for different subjective win probabilities, you get
something very much like a range ballot renormalized so that there is at
least one Smith set candidate at top and bottom. (It's not exactly that, the
math is more complex, especially when the Smith set is bigger than 3; but
it's a good enough approximation and much simpler than the exact answer).

Let's look at a few scenarios to see how this plays out.

First, the typical minimal Condorcet scenario. You have Va voters who say
A>B>C, and think on average that B is b% as good as A compared to C (that
is, if they rank them 70, 60, 20, then b=(60-20)/(70-20)=80%); Vb voters who
say B>C>A with C on average c% as good as B; and Vc voters who vote C>A>B
with A at a%. Without loss of generality, Va > Vb or Vc, but Va < Vb + Vc
(or A would be a Condorcet winner). The renormalized Range tiebreaking
scores are A=Va + a*Vc; B=Vb + b*Va; and C=Vc + c*Vb. What does that mean?
* If all of a, b, and c are 50%, then the candidate with the most
exceptionally strong win or weak loss, wins (that is, if the two strongest
wins are farther apart than the two weakest losses, then the strongest win,
otherwise the weakest loss).
* If one of a, b, and c is near 100% where the others are near 0%, then that
candidate wins. You could say that the XYZ voters' opinion of Y is acting as
the tiebreaker for Y.
* In general, for honest ballots, the winner is the candidate with the least
renormalized Bayesian regret. Assuming the effects of renormalization are
random, this will tend to be the candidate with the least Bayesian regret
overall.

Note that this could elect a Condorcet loser. For instance, if you had
ballots A>B>D>>>C, B>C>D>>>A, and C>A>D>>>B, (that is, each ballot rates
candidates at 100, 99, 98, and 0) then D is the Condorcet loser but has
higher utility than any other candidate, and wins. But this could only
happen if there is a Condorcet tie for winner. In general, I find the
scenario pretty implausible, and the result still optimal for that scenario.
(Because I think such results are optimal, I advocate using the Smith set
and not the Schwarz set for renormalizing).

How does this method do on other criteria? It fulfills Condorcet (by
definition) and is monotonic. For strategies which don't change the content
of the Smith set, it does very well on other criteria, fulfilling
Participation, Consistency, and "Local IIA". However, as the content of the
Smith set changes, it can fail all of those latter criteria - but only by
moving *towards* the renormalized utility winner, who is arguably the
correct winner anyway. I believe that, because of its construction, it will
have relatively low Bayesian Regret among Condorcet systems.

How resistant is it to strategy? When the Smith set is unchanged, all useful
strategies are at worst asymptotically on the honest side of semi-honest -
that is, they only require ranking equal (or, for nearly all of the
strategic benefit, nearly equal) candidates who are not honestly equal.
Moreover, I think that the DSV construction of this system gives it
excellent resistance to real-world strategies. Unless you have more
information than the agent which strategizes your ballot, you simply vote
honestly and allow the system to strategize for you. Thus, you wouldn't be
motivated to use strategy unless you felt you knew not only the exact
possibilities and chirality of the Smith set, both before and after your
strategizing, but also the probable winner from that Smith set. Under
realistic polling information, I think that such scenarios will be rare; if
you know of a possible Condorcet tie, then you will not generally know much
about the likely winners of this tie.

(It may even be provable that if you assume voters exist in some kind of
continuous, unimodal distribution in ideology space, and motivate Condorcet
ties by having non-euclidean but continuous distance measures, then there
will always naturally exist enough "honest defensive votes" to make any
strategy backfire).

Note that in regard to resisting simple strategies, this method is a serious
improvement over either Range or Approval. Because it is a kind of DSV, it
"does the strategy for you". So a candidate will gain no significant
advantage if their voters are more strategic (that is, more dichotomous and
better at evaluating the expected winners of the election) than other
candidates' voters. It allows for naive votes of many kinds, including
potentially "don't know" votes for certain candidates, simple approval-style
votes, simple ranking-style votes, and others, giving all approximately the
same power. And because it uses Range ballots as an input but encourages
more honest voting than Range, it enables the society to see (as an academic
question) who is the true Range winner, when that differs from the Condorcet
winner. I believe that, in successive elections, enough voters would
reevaluate such candidates to make one of them win in both senses.

Nonetheless, I will present one scenario where strategy might be employed.
Say the candidates are Nader, Gore, and Bush, and assume (contrafactually)
that this is simple a matter of 1-dimensional ideology and that all voters
agree that the candidates are, left to right,
nader..gore..........................bush (that is, Nader and Gore in this
scenario are considered much closer than Gore and Bush). Assume also that
there is some dearth of center-left voters who prefer Gore to Bush only
weakly. So the honest preferences are something like

Nader Gore Bush
11% 100 99 0
40% 99 100 0
49% 0 1 100

If all of the 11% of Nader voters dishonestly "bury" Gore under Bush, then
Nader wins with 50.6% (that is, 11% + (99%*40%)). However, if even 2 of the
40% Gore voters honestly vote Gore, Bush, Nader - or EVEN if those 2% simply
give Nader 1 point instead of 99 points - then the strategy backfires and
elects Bush. Given the honest utilities assumed, the Nader voters would not
use this strategy if they thought this was even 1% likely. In the real
election, of course, there was in fact a non-negligible minority of honest
Gore>Bush>Nader voters. (Gore voters were probably likelier to support Bush
second than Nader voters, and I've seen polls that say 1/4 of Nader voters
supported Bush second (!); 1/4 of Gore voters would be around 12%). So this
strategy would never have worked in real life, and in fact it requires an
artificial gap in the voter distribution right near the Gore>Bush>Nader zone
(extending on both sides of that zone, because for instance Gore>>Nader>Bush
votes hose the strategy too).
Paul Kislanko
2009-06-25 18:27:18 UTC
Permalink
I have a hard time reconciling "Note that this could elect a Condorcet
loser" and "It fulfills Condorcet (by definition) ".

If the first is true, the second cannot be, by, uhhh, definition.

_____

From: election-methods-***@lists.electorama.com
[mailto:election-methods-***@lists.electorama.com] On Behalf Of Jameson
Quinn
Sent: Thursday, June 25, 2009 12:56 PM
To: election-***@lists.electorama.com
Subject: [EM] Condorcet/Range DSV


I believe that using Range ballots, renormalized on the Smith set as a
Condorcet tiebreaker, is a very good system by many criteria. I'm of course
not
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-
January/014469.html> the first one to propose this method, but I'd like to
justify and analyze it further.


I call the system Condorcet/Range DSV because it can be conceived as a kind
of Declared Strategy Voting system, which rationally strategizes voters'
ballots for them assuming that they have correct but not-quite-complete
information about all other voters. Let me explain.

I have been looking into fully-rational DSV methods using Range ballots both
as input and as the underlying method in which strategies play out. It turns
out to be impossible, as far as I can tell, to get a stable, deterministic,
rational result from strategy when there is no Condorcet winner. (Assume
there's a stable result, A. Since A is not a cond. winner, there is some B
which beats A by a majority. If all B>A voters bullet vote for B then B is a
Condorcet winner, and so wins. Thus there exists an offensive strategy. This
proof is not fully general because it neglects defensive strategies, but in
practice trying to work out a coherent, stable DSV which includes defensive
strategies seems impossible to me.) Note that, on the other hand, there MUST
exist a stable probabilistic result, that is, a Nash equilibrium.

Let's take the case of a 3-candidate Smith set to start with. (This
simplifies things drastically and I've never seen a real-world example of a
larger set.) In the Nash equilibrium, all three candidates have a nonzero
probability of winning (or at least, are within one vote of having such a
probability). Voters are dissuaded from using offensive strategy by the real
probability that it would backfire and result in a worse candidate winning.
This Nash equilibrium is in some sense the "best" result, in that all voters
have equal power and no voter can strategically alter it. However, it is
both complicated-to-compute and unnecessarily probabilistic. Forest Simmons
has
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-
October/011028.html> proposed an interesting method for artificially
reducing the win probability of the less-likely candidates, but this method
increases computational complexity without being able to reach a single,
fully stable result. (Simmons proposed simply selecting the most-probable
candidate, which is probably the best answer, but it does invalidate the
whole strategic motivation).

There's an easier way. Simply assume that any given voter has only
near-perfect information, not perfect information. That is, each voter knows
exactly which candidates are in the Smith set, but makes an ideosyncratic
(random) evaluation of the probability of each of those candidates winning.
That voter's ideal strategic ballot is an approval style ballot in which all
candidates above their expected value are rated at the top and all
candidates below at the bottom. However, averaging over the different
ballots they'd give for different subjective win probabilities, you get
something very much like a range ballot renormalized so that there is at
least one Smith set candidate at top and bottom. (It's not exactly that, the
math is more complex, especially when the Smith set is bigger than 3; but
it's a good enough approximation and much simpler than the exact answer).

Let's look at a few scenarios to see how this plays out.

First, the typical minimal Condorcet scenario. You have Va voters who say
A>B>C, and think on average that B is b% as good as A compared to C (that
is, if they rank them 70, 60, 20, then b=(60-20)/(70-20)=80%); Vb voters who
say B>C>A with C on average c% as good as B; and Vc voters who vote C>A>B
with A at a%. Without loss of generality, Va > Vb or Vc, but Va < Vb + Vc
(or A would be a Condorcet winner). The renormalized Range tiebreaking
scores are A=Va + a*Vc; B=Vb + b*Va; and C=Vc + c*Vb. What does that mean?
* If all of a, b, and c are 50%, then the candidate with the most
exceptionally strong win or weak loss, wins (that is, if the two strongest
wins are farther apart than the two weakest losses, then the strongest win,
otherwise the weakest loss).
* If one of a, b, and c is near 100% where the others are near 0%, then that
candidate wins. You could say that the XYZ voters' opinion of Y is acting as
the tiebreaker for Y.
* In general, for honest ballots, the winner is the candidate with the least
renormalized Bayesian regret. Assuming the effects of renormalization are
random, this will tend to be the candidate with the least Bayesian regret
overall.

Note that this could elect a Condorcet loser. For instance, if you had
ballots A>B>D>>>C, B>C>D>>>A, and C>A>D>>>B, (that is, each ballot rates
candidates at 100, 99, 98, and 0) then D is the Condorcet loser but has
higher utility than any other candidate, and wins. But this could only
happen if there is a Condorcet tie for winner. In general, I find the
scenario pretty implausible, and the result still optimal for that scenario.
(Because I think such results are optimal, I advocate using the Smith set
and not the Schwarz set for renormalizing).

How does this method do on other criteria? It fulfills Condorcet (by
definition) and is monotonic. For strategies which don't change the content
of the Smith set, it does very well on other criteria, fulfilling
Participation, Consistency, and "Local IIA". However, as the content of the
Smith set changes, it can fail all of those latter criteria - but only by
moving *towards* the renormalized utility winner, who is arguably the
correct winner anyway. I believe that, because of its construction, it will
have relatively low Bayesian Regret among Condorcet systems.

How resistant is it to strategy? When the Smith set is unchanged, all useful
strategies are at worst asymptotically on the honest side of semi-honest -
that is, they only require ranking equal (or, for nearly all of the
strategic benefit, nearly equal) candidates who are not honestly equal.
Moreover, I think that the DSV construction of this system gives it
excellent resistance to real-world strategies. Unless you have more
information than the agent which strategizes your ballot, you simply vote
honestly and allow the system to strategize for you. Thus, you wouldn't be
motivated to use strategy unless you felt you knew not only the exact
possibilities and chirality of the Smith set, both before and after your
strategizing, but also the probable winner from that Smith set. Under
realistic polling information, I think that such scenarios will be rare; if
you know of a possible Condorcet tie, then you will not generally know much
about the likely winners of this tie.

(It may even be provable that if you assume voters exist in some kind of
continuous, unimodal distribution in ideology space, and motivate Condorcet
ties by having non-euclidean but continuous distance measures, then there
will always naturally exist enough "honest defensive votes" to make any
strategy backfire).

Note that in regard to resisting simple strategies, this method is a serious
improvement over either Range or Approval. Because it is a kind of DSV, it
"does the strategy for you". So a candidate will gain no significant
advantage if their voters are more strategic (that is, more dichotomous and
better at evaluating the expected winners of the election) than other
candidates' voters. It allows for naive votes of many kinds, including
potentially "don't know" votes for certain candidates, simple approval-style
votes, simple ranking-style votes, and others, giving all approximately the
same power. And because it uses Range ballots as an input but encourages
more honest voting than Range, it enables the society to see (as an academic
question) who is the true Range winner, when that differs from the Condorcet
winner. I believe that, in successive elections, enough voters would
reevaluate such candidates to make one of them win in both senses.

Nonetheless, I will present one scenario where strategy might be employed.
Say the candidates are Nader, Gore, and Bush, and assume (contrafactually)
that this is simple a matter of 1-dimensional ideology and that all voters
agree that the candidates are, left to right,
nader..gore..........................bush (that is, Nader and Gore in this
scenario are considered much closer than Gore and Bush). Assume also that
there is some dearth of center-left voters who prefer Gore to Bush only
weakly. So the honest preferences are something like

Nader Gore Bush
11% 100 99 0
40% 99 100 0
49% 0 1 100

If all of the 11% of Nader voters dishonestly "bury" Gore under Bush, then
Nader wins with 50.6% (that is, 11% + (99%*40%)). However, if even 2 of the
40% Gore voters honestly vote Gore, Bush, Nader - or EVEN if those 2% simply
give Nader 1 point instead of 99 points - then the strategy backfires and
elects Bush. Given the honest utilities assumed, the Nader voters would not
use this strategy if they thought this was even 1% likely. In the real
election, of course, there was in fact a non-negligible minority of honest
Gore>Bush>Nader voters. (Gore voters were probably likelier to support Bush
second than Nader voters, and I've seen polls that say 1/4 of Nader voters
supported Bush second (!); 1/4 of Gore voters would be around 12%). So this
strategy would never have worked in real life, and in fact it requires an
artificial gap in the voter distribution right near the Gore>Bush>Nader zone
(extending on both sides of that zone, because for instance Gore>>Nader>Bush
votes hose the strategy too).
Jameson Quinn
2009-06-25 18:37:49 UTC
Permalink
Post by Paul Kislanko
I have a hard time reconciling "Note that this could elect a Condorcet
loser" and "It fulfills Condorcet (by definition) ".
If the first is true, the second cannot be, by, uhhh, definition.
No. If there is a Condorcet winner, it elects that person; this is the
Condorcet criterion. If there is NO Condorcet winner, it could in some cases
elect someone who was not in the Smith set, including a Condorcet loser
(although, as I argued, that would generally still be the best person for
the job, as measured by utility, despite being the Condorcet loser).

The Condorcet criterion simply does not apply when there is no Condorcet
winner; it does not expand its purview to the Smith set.

Jameson
Jameson Quinn
2009-06-25 19:53:45 UTC
Permalink
I left out one good aspect of this system. It is additive - ie, it can be
counted locally. You need to keep n(n-1)(n-1)/2 tallies - the Condorcet
matrix, plus the result of each candidate renormalized against every other
pair of candidates. If there were ever more than 3 candidates in the Smith
set, you could reconstruct the multiway-renormalized totals from linear
combinations of the summed 3-way-renormalized totals.
If you are willing to do one and a half counting rounds (that is, one
definitely and then another one if there's no Condorcet winner), then you
keep n(n-1)/2 tallies in the first round and n tallies in the second round.

Generally, I'd support ballot access hurdles to keep it down to around 4-6
candidates per election. That's 18-90 tallies for one-round counting, or
10-36 for one-and-a-half-rounds.

The system is also pretty easy to explain. "You rank each candidate from 0
to 100. If one candidate beats each of the others one-on-one, they win. If
not, you ignore all the loser candidates who only beat other losers. Then,
to give everybody's vote full power, you set their favorite winner candidate
to 100 and their least favorite winner to 0, leaving the spacing of the
choices in between the same. You add together each candidate's rating on all
these fixed-up ballots and whichever candidate has the highest overall
rating wins.

"As a voter, unless you think there will be no clear winner AND you know
exactly who will beat whom, there's no reason to be anything less than
perfectly honest, because the system fixes up your ballot to give it full
power in the decisive runoff. If you do try to beat the system and you're
wrong, it will backfire; the safest ballot is your honest vote. You don't
even have to be too careful about giving everyone exact ratings, because it
only matters if there's not just a *two* way tie but actually a close tie
between at least *three* strong candidates, which is very rare."

(When Condorcet methods have more of a political track record, we'll be able
to start saying how rare. With random ballots between 3 candidates, it's
about 9% probable; since most elections do not have 3 equally-strong
frontrunners, it should be much rarer than that in practice.)
Chris Benham
2009-06-26 14:32:39 UTC
Permalink
Jameson,

This Condorcet-Range hybrid you suggest seems to me to inherit a couple of
the problems with Range Voting.

It fails the Minimal Defense criterion.

49: A100,  B0,  C0
24: B100,  A0,  C0
27: C100,  B80, A0

More than half the voters vote A not above equal-bottom and below B, and yet
A wins.

Also I don't like the fact that the result can be affected just by varying the resolution
of  ratings ballots used, an arbitrary feature.

I think it would be better if the method derived approval from the ballots, approving all
candidates the voter rates above the voter's average rating of  the Smith set members.


"For strategies which don't change the content
of the Smith set, it does very well on other criteria, fulfilling
Participation, Consistency, and "Local IIA". "


The criteria you mention only apply (as a strict pass/fail test) to voting methods, not
"strategies" (and  have nothing to do with strategy).

We know that Condorcet is incompatible with Participation  (and so I suppose also with
the similar Consistency).  I don't see how a method that fails Condorcet Loser can meet
Local IIA.

"And because it uses Range ballots as an input but encourages
more honest voting than Range,.."

That is more true of the "automated approval" version I suggested, and also it isn't
completely clear-cut because Range meets Favourite Betrayal which is incompatible
with Condorcet.

 
Chris Benham


Jameson Quinn wrote (25 June 2009) wrote:

________________________________
 
I believe that using Range ballots, renormalized on the Smith set as a
Condorcet tiebreaker, is a very good system by many criteria. I'm of course
not<http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-January/014469.html>the
first one to propose this method, but I'd like to justify and analyze
it further.

I call the system Condorcet/Range DSV because it can be conceived as a kind of
Declared Strategy Voting system, which rationally strategizes voters' ballots for them assuming that
they have correct but not-quite-complete information about all other voters.
Let me explain.

I have been looking into fully-rational DSV methods using Range ballots both
as input and as the underlying method in which strategies play out. It turns
out to be impossible, as far as I can tell, to get a stable, deterministic,
rational result from strategy when there is no Condorcet winner. (Assume
there's a stable result, A. Since A is not a cond. winner, there is some B
which beats A by a majority. If all B>A voters bullet vote for B then B is a
Condorcet winner, and so wins. Thus there exists an offensive strategy. This
proof is not fully general because it neglects defensive strategies, but in
practice trying to work out a coherent, stable DSV which includes defensive
strategies seems impossible to me.) Note that, on the other hand, there MUST
exist a stable probabilistic result, that is, a Nash equilibrium.

Let's take the case of a 3-candidate Smith set to start with. (This
simplifies things drastically and I've never seen a real-world example of a
larger set.) In the Nash equilibrium, all three candidates have a nonzero
probability of winning (or at least, are within one vote of having such a
probability). Voters are dissuaded from using offensive strategy by the real
probability that it would backfire and result in a worse candidate winning.
This Nash equilibrium is in some sense the "best" result, in that all voters
have equal power and no voter can strategically alter it. However, it is
both complicated-to-compute and unnecessarily probabilistic. Forest Simmons has
proposed an interesting
method<http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011028.html>for
artificially reducing the win probability of the less-likely
candidates,
but this method increases computational complexity without being able to
reach a single, fully stable result. (Simmons proposed simply selecting the
most-probable candidate, which is probably the best answer, but it does
invalidate the whole strategic motivation).
There's an easier way. Simply assume that any given voter has only
near-perfect information, not perfect information. That is, each voter knows
exactly which candidates are in the Smith set, but makes an ideosyncratic
(random) evaluation of the probability of each of those candidates winning.
That voter's ideal strategic ballot is an approval style ballot in which all
candidates above their expected value are rated at the top and all
candidates below at the bottom. However, averaging over the different
ballots they'd give for different subjective win probabilities, you get
something very much like a range ballot renormalized so that there is at
least one Smith set candidate at top and bottom. (It's not exactly that, the
math is more complex, especially when the Smith set is bigger than 3; but
it's a good enough approximation and much simpler than the exact answer).

Let's look at a few scenarios to see how this plays out.

First, the typical minimal Condorcet scenario. You have Va voters who say
A>B>C, and think on average that B is b% as good as A compared to C (that
is, if they rank them 70, 60, 20, then b=(60-20)/(70-20)=80%); Vb voters who
say B>C>A with C on average c% as good as B; and Vc voters who vote C>A>B
with A at a%. Without loss of generality, Va > Vb or Vc, but Va < Vb + Vc
(or A would be a Condorcet winner). The renormalized Range tiebreaking
scores are A=Va + a*Vc; B=Vb + b*Va; and C=Vc + c*Vb. What does that mean?
* If all of a, b, and c are 50%, then the candidate with the most
exceptionally strong win or weak loss, wins (that is, if the two strongest
wins are farther apart than the two weakest losses, then the strongest win,
otherwise the weakest loss).
* If one of a, b, and c is near 100% where the others are near 0%, then that
candidate wins. You could say that the XYZ voters' opinion of Y is acting as
the tiebreaker for Y.
* In general, for honest ballots, the winner is the candidate with the least
renormalized Bayesian regret. Assuming the effects of renormalization are
random, this will tend to be the candidate with the least Bayesian regret
overall.

Note that this could elect a Condorcet loser. For instance, if you had
ballots A>B>D>>>C, B>C>D>>>A, and C>A>D>>>B, (that is, each ballot rates
candidates at 100, 99, 98, and 0) then D is the Condorcet loser but has
higher utility than any other candidate, and wins. But this could only
happen if there is a Condorcet tie for winner. In general, I find the
scenario pretty implausible, and the result still optimal for that scenario.
(Because I think such results are optimal, I advocate using the Smith set
and not the Schwarz set for renormalizing).

How does this method do on other criteria? It fulfills Condorcet (by
definition) and is monotonic. For strategies which don't change the content
of the Smith set, it does very well on other criteria, fulfilling
Participation, Consistency, and "Local IIA". However, as the content of the
Smith set changes, it can fail all of those latter criteria - but only by
moving *towards* the renormalized utility winner, who is arguably the
correct winner anyway. I believe that, because of its construction, it will
have relatively low Bayesian Regret among Condorcet systems.

How resistant is it to strategy? When the Smith set is unchanged, all useful
strategies are at worst asymptotically on the honest side of semi-honest -
that is, they only require ranking equal (or, for nearly all of the
strategic benefit, nearly equal) candidates who are not honestly equal.
Moreover, I think that the DSV construction of this system gives it
excellent resistance to real-world strategies. Unless you have more
information than the agent which strategizes your ballot, you simply vote
honestly and allow the system to strategize for you. Thus, you wouldn't be
motivated to use strategy unless you felt you knew not only the exact
possibilities and chirality of the Smith set, both before and after your
strategizing, but also the probable winner from that Smith set. Under
realistic polling information, I think that such scenarios will be rare; if
you know of a possible Condorcet tie, then you will not generally know much
about the likely winners of this tie.

(It may even be provable that if you assume voters exist in some kind of
continuous, unimodal distribution in ideology space, and motivate Condorcet
ties by having non-euclidean but continuous distance measures, then there
will always naturally exist enough "honest defensive votes" to make any
strategy backfire).

Note that in regard to resisting simple strategies, this method is a serious
improvement over either Range or Approval. Because it is a kind of DSV, it
"does the strategy for you". So a candidate will gain no significant
advantage if their voters are more strategic (that is, more dichotomous and
better at evaluating the expected winners of the election) than other
candidates' voters. It allows for naive votes of many kinds, including
potentially "don't know" votes for certain candidates, simple approval-style
votes, simple ranking-style votes, and others, giving all approximately the
same power. And because it uses Range ballots as an input but encourages
more honest voting than Range, it enables the society to see (as an academic
question) who is the true Range winner, when that differs from the Condorcet
winner. I believe that, in successive elections, enough voters would
reevaluate such candidates to make one of them win in both senses.

Nonetheless, I will present one scenario where strategy might be employed.
Say the candidates are Nader, Gore, and Bush, and assume (contrafactually)
that this is simple a matter of 1-dimensional ideology and that all voters
agree that the candidates are, left to right,
nader..gore..........................bush (that is, Nader and Gore in this
scenario are considered much closer than Gore and Bush). Assume also that
there is some dearth of center-left voters who prefer Gore to Bush only
weakly. So the honest preferences are something like

               Nader  Gore  Bush
11%         100      99      0
40%         99        100    0
49%         0          1       100

If all of the 11% of Nader voters dishonestly "bury" Gore under Bush, then
Nader wins with 50.6% (that is, 11% + (99%*40%)). However, if even 2 of the
40% Gore voters honestly vote Gore, Bush, Nader - or EVEN if those 2% simply
give Nader 1 point instead of 99 points - then the strategy backfires and
elects Bush. Given the honest utilities assumed, the Nader voters would not
use this strategy if they thought this was even 1% likely. In the real
election, of course, there was in fact a non-negligible minority of honest
Gore>Bush>Nader voters. (Gore voters were probably likelier to support Bush
second than Nader voters, and I've seen polls that say 1/4 of Nader voters
supported Bush second (!); 1/4 of Gore voters would be around 12%). So this
strategy would never have worked in real life, and in fact it requires an
artificial gap in the voter distribution right near the Gore>Bush>Nader zone
(extending on both sides of that zone, because for instance Gore>>Nader>Bush
votes hose the strategy too).
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Jameson Quinn
2009-06-26 23:04:46 UTC
Permalink
Post by Chris Benham
This Condorcet-Range hybrid you suggest seems to me to inherit a couple of
the problems with Range Voting.
Fair enough.
Post by Chris Benham
It fails the Minimal Defense criterion.
49: A100, B0, C0
24: B100, A0, C0
27: C100, B80, A0
More than half the voters vote A not above equal-bottom and below B, and yet
A wins.
True. Yet B could win if the C voters rated B 99, which would still be
Condorcet-honest.
Post by Chris Benham
Also I don't like the fact that the result can be affected just by varying the resolution
of ratings ballots used, an arbitrary feature.
I think it would be better if the method derived approval from the ballots, approving all
candidates the voter rates above the voter's average rating of the Smith
set members.
That is not a bad suggestion; I like both systems. Yours gives less of a
motivation for honest rating: In most cases, it makes A100 B99 C0 equivalent
to A100 B51 C0. I guess you'd give exactly half an approval if B were at
exactly 50?

Anyway, the main motivations for a DSV-type proposal like this is to make it
really rare for voters to have enough information to strategize without it
backfiring. I think that including full range information (that is, my
proposal as opposed to yours) makes the voter's analysis harder, and so
makes the system more resistant to strategy. Under honest range votes, it
also helps improve the utility.
Post by Chris Benham
"For strategies which don't change the content
of the Smith set, it does very well on other criteria, fulfilling
Participation, Consistency, and "Local IIA". "
Sorry, I wasn't clear. If the content of the smith set DOES change, this
method fails all those criteria. See below for argument of why that's not
too bad.
Post by Chris Benham
"And because it uses Range ballots as an input but encourages
more honest voting than Range,.."
That is more true of the "automated approval" version I suggested, and also it isn't
completely clear-cut because Range meets Favourite Betrayal which is incompatible
with Condorcet.
Favorite Betrayal in this case means, honest ABC voters who know that A's
losing and that C>B>>A and A>>C>B votes are both relatively common, can vote
BAC to cause a Condorcet tie and perhaps get B to win (if A would win that
tie, then A would be winning already, so they can't get their favorite
through betrayal. In other words, at least it's monotonic.). But if they
bring on the Condorcet tie, they are also risking C winning if there are
more C>>B>A votes than C>B>>A votes. (Of course they're also risking having
been wrong and throwing away an A win, though that's the nature of favorite
betrayal and scarcely bears mentioning.) If they are even considering
favorite betrayal, they probably feel A>B>>C, so even a small risk of C
should be a strong deterrent.

In other words, the whole point of this system is that honesty is the safest
strategy. If voters are even moderately risk-averse and information is
anything less than perfect, the system (and your alternate version proposal)
is, I believe, unparallelled for its strategy resistence. If voters are
risk-seekers and enjoy attempting strategy, then it's no worse than
min(condorcet, approval), which is both IMO implausible and really not too
bad anyway.

Jameson
Chris Benham
2009-07-01 17:39:09 UTC
Permalink
Jameson,

Sorry to be so tardy in replying.

 
"That is not a bad suggestion; I like both systems. Yours gives less of a motivation for
honest rating: In most cases, it makes A100 B99 C0 equivalent to A100 B51 C0."

No, mine gives more motivation for honest rating (in the sense that it gives less incentive
for dishonest rating).   If  A, B, C  are the three Smith-set members then it makes both
A100, B99, C0 and  A100, B51, C0  equivalent to A100, B100, C0.

"I guess you'd give exactly half an approval if B were at exactly 50?"

Yes.

49: A100,  B0,  C0
24: B100,  A0,  C0
27: C100,  B80, A0

More than half the voters vote A not above equal-bottom and below B, and yet
A wins.

"True. Yet B could win if the C voters rated B 99, which would still be Condorcet-honest."

That isn't really in principle relevant because your suggested method doesn't guarantee to a
section of the voters comprising more than half  who rate/rank A bottom that they can ensure
that A loses while still expressing all their sincere pairwise preferences.

4999: A100,  B0,  C0
2500: B100,  A0,  C0
2501: C100,  B99, A0

B>A 5001- 4999,  A>C,  C>B.    

In this modified version of my demonstration that your suggested method fails Minimal Defense,
the majority that prefer B to A cannot ensure that B loses and still be "Condorcet-honest".

"Anyway, the main motivations for a DSV-type proposal like this is to make it really rare for voters
to have enough information to strategize without it backfiring. I think that including full range information
(that is, my proposal as opposed to yours) makes the voter's analysis harder, and so makes the system  
more resistant to strategy."

I don't think the type of examples I've given would be "really rare", and in them I don't think the C
supporters have to very well-informed or clever to work out that their candidate can't beat A and
so they have incentive to falsely vote B (at least) equal to their favourite.

"Favorite Betrayal in this case means, honest ABC voters who know that A's losing and that C>B>>A
and A>>C>B votes are both relatively common, can vote BAC to cause a Condorcet tie and perhaps
get B to win ..."

Not necessarily, no. You seem to be assuming that Favourite Betrayal strategy is only about falsely creating
a  "Condorcet tie" when one's favourite isn't the (presumed to be) sincere Condorcet winner. It can
also be the case that the strategist fears that if she votes sincerely there will be no Condorcet winner,
so she order-reverse compromises to try to make her compromise the voted Condorcet winner.


Chris  Benham





________________________________

Jameson Quinn wrote  (26 June 2009) :


This Condorcet-Range hybrid you suggest seems to me to inherit a couple of
Post by Chris Benham
the problems with Range Voting.
Fair enough.
Post by Chris Benham
It fails the Minimal Defense criterion.
49: A100,  B0,  C0
24: B100,  A0,  C0
27: C100,  B80, A0
More than half the voters vote A not above equal-bottom and below B, and yet
A wins.
True. Yet B could win if the C voters rated B 99, which would still be Condorcet-honest.
Post by Chris Benham
Also I don't like the fact that the result can be affected just by varying the resolution
of  ratings ballots used, an arbitrary feature.
I think it would be better if the method derived approval from the ballots, approving all
candidates the voter rates above the voter's average rating of  the Smith set members.
That is not a bad suggestion; I like both systems. Yours gives less of a motivation for honest rating: In most cases, it makes A100 B99 C0 equivalent to A100 B51 C0. I guess you'd give exactly half an approval if B were at exactly 50?

Anyway, the main motivations for a DSV-type proposal like this is to make it really rare for voters to have enough information to strategize without it backfiring. I think that including full range information (that is, my proposal as opposed to yours) makes the voter's analysis harder, and so makes the system  more resistant to strategy. Under honest range votes, it also helps improve the utility.
Post by Chris Benham
"For strategies which don't change the content
of the Smith set, it does very well on other criteria, fulfilling
Participation, Consistency, and "Local IIA". "
Sorry, I wasn't clear. If the content of the smith set DOES change, this method fails all those criteria. See below for argument of why that's not too bad.
Post by Chris Benham
"And because it uses Range ballots as an input but encourages
more honest voting than Range,.."
That is more true of the "automated approval" version I suggested, and also it isn't
completely clear-cut because Range meets Favourite Betrayal which is incompatible
with Condorcet.
Favorite Betrayal in this case means, honest ABC voters who know that A's losing and that C>B>>A and A>>C>B votes are both relatively common, can vote BAC to cause a Condorcet tie and perhaps get B to win (if A would win that tie, then A would be winning already, so they can't get their favorite through betrayal. In other words, at least it's monotonic.). But if they bring on the Condorcet tie, they are also risking C winning if there are more C>>B>A votes than C>B>>A votes. (Of course they're also risking having been wrong and throwing away an A win, though that's the nature of favorite betrayal and scarcely bears mentioning.) If they are even considering favorite betrayal, they probably feel A>B>>C, so even a small risk of C should be a strong deterrent.

In other words, the whole point of this system is that honesty is the safest strategy. If voters are even moderately risk-averse and information is anything less than perfect, the system (and your alternate version proposal) is, I believe, unparallelled for its strategy resistence. If voters are risk-seekers and enjoy attempting strategy, then it's no worse than min(condorcet, approval), which is both IMO implausible and really not too bad anyway.

Jameson


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Dave Ketchum
2009-07-01 03:57:08 UTC
Permalink
Food for thought:

The "National Popular Vote" effort is a proper attempt to hear voters
better in electing a President - votes from all states would get
counted, unlike the present problem that, in many states, all of the
states electoral votes will go to the known and expected winner of
that state's voting - which, in turn, discourages candidates from
being much concerned with trying to increase their vote count from
such states.

But, how should the votes be counted when merging the votes from
multiple states? I suspect Plurality is expected because all states
know how to do that.

How about Condorcet? It lets voters express themselves more
completely, but then we have to be concerned with some states not
being prepared to do Condorcet electing.

I propose here that that is not a proper concern. Condorcet, of
course, counts, merging together votes:
as in Plurality - and thus could count in votes from states
offering only Plurality.
as in Approval - assuming, as is proper, that such could be
voted in real Condorcet.
of what Condorcet offers.

Knowing what a voter votes in Plurality or Approval, the counters
simply count what would have been counted for the voter if the voter
had voted such in a Condorcet election.

This both allows merging together what different states may be
prepared to offer, and gives them a path toward general use of
Condorcet - a tolerable destination.

Admittedly this ignores such as Range and Borda - but gives voters
better power than Plurality, while minimizing what new they could be
asked to learn.

Note that Condorcet is more tolerant than most, of different sets of
candidates being offered in different states. Conceded that such is
undesirable but, assuming Condorcet, voters can both vote what is
generally agreed on as to expectable winners, and what odd may be
added for their state.

Dave Ketchum


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Paul Kislanko
2009-07-01 05:44:46 UTC
Permalink
The idea is a good one, but there's no practical way to make it work.

If all you have is plurality counts, you don't have enough information to
retrieve the voters' Condorcet pairwise preferences. If what you mean is use
States' plurality results to form a condorcet matrix, you get even worse
than what we have now since that results in each state getting a condorcet
vote regardless of the number of voters in each state.

I'm sure that's not what you meant, but this allows me to re-introduce
something I suggested several years ago. If somehow we could define an
"election method" as a combination of "vote collection process" and "vote
counting process" we could select a collection method that would support any
known counting process.

One can infer a plurality ballot from any kind of ranked ballot, but not the
other way around.

One can infer an approval ballot from any kind of ranked ballot that allows
equal ranks, but not the other way around.

"Any kind of ranked ballot" includes a range ballot, since an ordinal
ranking (allowing equal ranks) can be obtained by sorting the alternatives
on each ballot by their values. One can NOT retrieve the range from an
ordinal ranking derived from the voter's range ballot, but that is only a
problem if the global counting is range. If that's the case all states must
use range ballots and there's no problem.

If every ballot is a ranked ballot, we can choose a COUNTING process that is
plurality, approval, or Condorcet. We can even (and probably should) use a
Condorcet COUNTING process to process range ballots, instead of just summing
values over altertanitives.

But the most general COLLECTION process would be a "Condoret ballot", where
the voter is presented EACH pair of alternatives and asked to pick one. For
instance, in the {A B C} case instead of having to pick ONE from:
A>B>C
A>C>B
B>A>C
B>C>A
C>A>B
C>B>A
But if I got to choose my own pairwise preferences:
A > B or B > A
A > C or C > A
B > C or C > B
I might have come up with A>B B>C and C>A, which can't be put into a ranked
ballot because you can't have A>B>C>A, but that was my sincere Condorcet
vote. There's no way you can use Condercet COUNTING to find voter
preferences if you don't use a Connoret BALLOT to collect all the votes.

Which means nothing except to count popular vote across all states you have
to use the LEAST representative BALLOT representation across ALL states,
which is plurality (sigh.)

FWIW there's a movement gaining traction for each State to assign its
electors to the winner of the NATIONAL popular vote. Bad as it may be,
Plurality may save us yet.








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Jonathan Lundell
2009-07-01 14:22:37 UTC
Permalink
Post by Paul Kislanko
One can infer a plurality ballot from any kind of ranked ballot, but not the
other way around.
One can infer an approval ballot from any kind of ranked ballot that allows
equal ranks, but not the other way around.
Except for strategic considerations. There are surely many cases in
which my plurality vote is not the same as my first-ranked vote under,
say, IRV or a Condorcet method.
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Paul Kislanko
2009-07-01 14:35:06 UTC
Permalink
Yes, as usual I wasn't very clear. The way that SHOULD have been worded is:

One can use plurality to count any kind of ranked ballots, but only
plurality to count plurality ballots.

One can use approval to count any kind of ranked ballots that allow equal
rankings, but only approval to count approval ballots.

My point being that if we used the most general kind of ballot, the
COLLECTION process is independent of the COUNTING method. Which, in a way
avoids the whole strategy discussion. If I'm asked to fill out a ranked
ballot without knowing how it will be counted, I can't "strategically" vote
"insincerely."

It's more a technique for formalizing analysis, not a recommendation.

-----Original Message-----
From: Jonathan Lundell [mailto:***@pobox.com]
Sent: Wednesday, July 01, 2009 9:23 AM
To: Paul Kislanko
Cc: 'Dave Ketchum'; 'EM'
Subject: Re: [EM] National Popular Vote & Condorcet
Post by Paul Kislanko
One can infer a plurality ballot from any kind of ranked ballot, but not the
other way around.
One can infer an approval ballot from any kind of ranked ballot that allows
equal ranks, but not the other way around.
Except for strategic considerations. There are surely many cases in
which my plurality vote is not the same as my first-ranked vote under,
say, IRV or a Condorcet method.


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Bob Richard
2009-07-01 14:50:58 UTC
Permalink
... avoids the whole strategy discussion. If I'm asked to fill out
a ranked ballot without knowing how it will be counted, I can't
"strategically" vote "insincerely."
I would say that I can't vote at all and would probably boycott the election.
It's more a technique for formalizing analysis, not a recommendation.
Yes.

--Bob Richard
One can use plurality to count any kind of ranked ballots, but only
plurality to count plurality ballots.
One can use approval to count any kind of ranked ballots that allow equal
rankings, but only approval to count approval ballots.
My point being that if we used the most general kind of ballot, the
COLLECTION process is independent of the COUNTING method. Which, in a way
avoids the whole strategy discussion. If I'm asked to fill out a ranked
ballot without knowing how it will be counted, I can't "strategically" vote
"insincerely."
It's more a technique for formalizing analysis, not a recommendation.
-----Original Message-----
Sent: Wednesday, July 01, 2009 9:23 AM
To: Paul Kislanko
Cc: 'Dave Ketchum'; 'EM'
Subject: Re: [EM] National Popular Vote & Condorcet
Post by Paul Kislanko
One can infer a plurality ballot from any kind of ranked ballot, but not the
other way around.
One can infer an approval ballot from any kind of ranked ballot that allows
equal ranks, but not the other way around.
Except for strategic considerations. There are surely many cases in
which my plurality vote is not the same as my first-ranked vote under,
say, IRV or a Condorcet method.
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--
Bob Richard
Executive Vice President
Californians for Electoral Reform
P.O. Box 235
Kentfield, CA 94914-0235
415-256-9393
http://www.cfer.org

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Dave Ketchum
2009-07-01 21:34:01 UTC
Permalink
Now it is July 1 and I have responses from ***@airmail.net, ***@pobox.com
, Markus Schulze.

Merging is possible, provided each state provides and describes data
suitable for this purpose, such as:
Condorcet X*X array. Because of possibility of extra candidates
from some states, each state should be required to include data for a
dummy candidate who gets no votes in that state - such can be included
for each such extra candidate.
Plurality data - suitable for both states which do Plurality,
and for those who use some method not provided for. For such an X*X
array is filled out with data as if votes reported had been reported
for the candidate strictly preferred by each of the state's voters -
and entered in the X*X array as if voted in Condorcet.
Approval data - needs thought but my initial thought is as if
each approval was a plurality vote - does mean a voter approving 2
gets 2 votes counted but relative counts per candidate comes out ok.
IRV or Range - examples of methods that should be avoided by
states willing to have their data included - unless they are willing
and able to convert to a method that is supported.

Some question merging data from different types of sources - I claim
it is doable provided the source type is provided for and the data
properly labelled.

Markus Schulze says to use the Schulze method for cycles - that should
be considered when agreeing on details. I would add that there should
be ONE X*X array for the US for this purpose, so that all cooperating
states give the same instructions to their electors.
Post by Dave Ketchum
The "National Popular Vote" effort is a proper attempt to hear
voters better in electing a President - votes from all states would
get counted, unlike the present problem that, in many states, all of
the states electoral votes will go to the known and expected winner
of that state's voting - which, in turn, discourages candidates from
being much concerned with trying to increase their vote count from
such states.
But, how should the votes be counted when merging the votes from
multiple states? I suspect Plurality is expected because all states
know how to do that.
How about Condorcet? It lets voters express themselves more
completely, but then we have to be concerned with some states not
being prepared to do Condorcet electing.
I propose here that that is not a proper concern. Condorcet, of
as in Plurality - and thus could count in votes from states
offering only Plurality.
as in Approval - assuming, as is proper, that such could be
voted in real Condorcet.
of what Condorcet offers.
Knowing what a voter votes in Plurality or Approval, the counters
simply count what would have been counted for the voter if the voter
had voted such in a Condorcet election.
This both allows merging together what different states may be
prepared to offer, and gives them a path toward general use of
Condorcet - a tolerable destination.
Admittedly this ignores such as Range and Borda - but gives voters
better power than Plurality, while minimizing what new they could be
asked to learn.
Note that Condorcet is more tolerant than most, of different sets of
candidates being offered in different states. Conceded that such is
undesirable but, assuming Condorcet, voters can both vote what is
generally agreed on as to expectable winners, and what odd may be
added for their state.
Dave Ketchum
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Raph Frank
2009-07-02 16:35:20 UTC
Permalink
Approval data - needs thought but my initial thought is as if each
approval was a plurality vote - does mean a voter approving 2 gets 2 votes
counted but relative counts per candidate comes out ok.
IRV or Range - examples of methods that should be avoided by states
willing to have their data included - unless they are willing and able to
convert to a method that is supported.
I would group them as

Plurality:
A vote for candidate A is considered
A>(others)

Condorcet:
Matrix is provided directly

IRV:
Extract as much info as possible, for example

Round 1:
A: 100
B: 82
C: 41
D: 13

100: A>(others)
82: B>(others)
41: C>(others)
13: D>(others)

D elliminated
4 go to A
3 go to B
5 go to C
1 untransferable

Votes are now
100: A>(others)
82: B>(others)
41: C>(others)
4: D>A>(others)
3: D>B>(others)
5: D>C>(others)
1: D (so effectively D>(others)

C would then be eliminated and we would get info about 2nd choices for
C. One issue here is that C>D>A would not be distinguished from C>A
(as both would transfer to A).

Approval/Range

This are somewhat different versions of the same method. There isn't
any way to reverse the process back to votes.

You give each candidate a plurality vote of (votes obtained)*[votes
cast/total approval]. This would at least mean that the state
wouldn't be over represented.

If there were 1000 votes cast and the results were

A: 800
B: 400
C: 300
Total 1500

Then, the results would be:

A: 800/1.5 = 533
B: 400/1.5 = 267
C: 300/1.5 = 200

I you assume that voters will use the strategy of vote for their
favourite of the top-2 and all they prefer to the expected winner, you
could estimate the preference table.

It is possible to find a matrix that matches the approval results, but
there wouldn't be a unique one.

For example:

"Add" A's 800 approvals
800: A
200:

"Add" B's 400 approvals

800 split into:
480: A
320: A+B

200 split into
120:
80: B

Total
480: A
320: A+B
120:
80: B

and so on.

That would result in an assumption that lots of votes cast blank votes.

Another option would be to find the "top-2". This could be the 2 most
approved candidates, W (winner) and S (second).

It is assumed that W and S voters would not approve each other to the
greatest extend possible.

So, the above example becomes
A: 800
B: 400
C: 300
Total 1500

A and B are top-2, if 800 approved A and 400 approved B, then at least
200 must have approved both. This assumes

600: A
200: A+B
200: B

This means that every voter is assumed to approve one of the top-2.

The rest of the candidates could then be assumed to be random.

The full process would be

1) Assume all ballots are blank
2) Process Candidates from most to least approved
3) If any ballots are blank, then designate them as approving the
current candidate
4) Distribute any remaining approval for the candidate randomly
5) Goto 2

This gets you a set of approval ballots which is consistant with the
results. Also, it is likely to be reasonably accurate, based on the
assumption that each voter only approves one of the top-2.

It can be gamed if a party runs 2 candidates, as then every voter is
considered to vote for one of their candidates.

One option would be to fill blank ballots and then ballots approved by
all the other candidates (bar the most approved).
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Dave Ketchum
2009-07-02 21:03:56 UTC
Permalink
On Wed, Jul 1, 2009 at 10:34 PM, Dave
Approval data - needs thought but my initial thought is as if each
approval was a plurality vote - does mean a voter approving 2 gets 2 votes
counted but relative counts per candidate comes out ok.
IRV or Range - examples of methods that should be avoided by states
willing to have their data included - unless they are willing and able to
convert to a method that is supported.
To summarize my thinking:

Each state controls how it interacts with its voters - so let them
choose their own way, such that their voters' desires get properly
added into the national X*X array.
I would group them as
A vote for candidate A is considered
A>(others)
This reads as giving the same power as if ranking ONE candidate in
Condorcet - simple and declarably accurate.
Matrix is provided directly
Here the voters could have ranked exactly as in Condorcet, but
standard IRV counting does not extract all that the voters say. I
would leave it to the state - perhaps they will do an X*X matrix. I
do not like what I read below - better for such states to avoid such
as IRV when they do not fit with what is reasonably the standard.
Summary: Presumably this state does IRV for races it controls. It's
voters, and those thinking in other states, would like something other
than what follows for this race in this state.
Extract as much info as possible, for example
A: 100
B: 82
C: 41
D: 13
100: A>(others)
82: B>(others)
41: C>(others)
13: D>(others)
D elliminated
4 go to A
3 go to B
5 go to C
1 untransferable
Votes are now
100: A>(others)
82: B>(others)
41: C>(others)
4: D>A>(others)
3: D>B>(others)
5: D>C>(others)
1: D (so effectively D>(others)
C would then be eliminated and we would get info about 2nd choices for
C. One issue here is that C>D>A would not be distinguished from C>A
(as both would transfer to A).
Approval/Range
For approval my first thought is that they are presumably doing
approval and my first choice for them is whatever Condorcet states do
when their voters vote with approval thinking.

For Range the thinking is much as I do above for IRV.
This are somewhat different versions of the same method. There isn't
any way to reverse the process back to votes.
You give each candidate a plurality vote of (votes obtained)*[votes
cast/total approval]. This would at least mean that the state
wouldn't be over represented.
If there were 1000 votes cast and the results were
A: 800
B: 400
C: 300
Total 1500
A: 800/1.5 = 533
B: 400/1.5 = 267
C: 300/1.5 = 200
I you assume that voters will use the strategy of vote for their
favourite of the top-2 and all they prefer to the expected winner, you
could estimate the preference table.
It is possible to find a matrix that matches the approval results, but
there wouldn't be a unique one.
"Add" A's 800 approvals
800: A
"Add" B's 400 approvals
480: A
320: A+B
200 split into
80: B
Total
480: A
320: A+B
80: B
and so on.
That would result in an assumption that lots of votes cast blank votes.
Another option would be to find the "top-2". This could be the 2 most
approved candidates, W (winner) and S (second).
It is assumed that W and S voters would not approve each other to the
greatest extend possible.
So, the above example becomes
A: 800
B: 400
C: 300
Total 1500
A and B are top-2, if 800 approved A and 400 approved B, then at least
200 must have approved both. This assumes
600: A
200: A+B
200: B
This means that every voter is assumed to approve one of the top-2.
The rest of the candidates could then be assumed to be random.
The full process would be
1) Assume all ballots are blank
2) Process Candidates from most to least approved
3) If any ballots are blank, then designate them as approving the
current candidate
4) Distribute any remaining approval for the candidate randomly
5) Goto 2
This gets you a set of approval ballots which is consistant with the
results. Also, it is likely to be reasonably accurate, based on the
assumption that each voter only approves one of the top-2.
It can be gamed if a party runs 2 candidates, as then every voter is
considered to vote for one of their candidates.
One option would be to fill blank ballots and then ballots approved by
all the other candidates (bar the most approved).
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Paul Kislanko
2009-07-02 21:23:29 UTC
Permalink
Without going into detail, if all states do not use the same collection
method, applying a national counting method that isn't the "lowest common
denominator" method, there would be a violation of the "equal process"
clause of the 14th Amendment. In order to use a ranked-ballot method, every
state would have to provide ranked BALLOTS to be counted.

What we have now is we can "roll up" from precinct to district to state to
national only SUMS, because everybody counts ballots the same way. If state
X counts ballots differently than state Y, we can't just "add" X and Y in
the national total without running afoul of the 14th Amendment.

Even though "I am not a lawyer", I know some who would bring that up.

-----Original Message-----
From: election-methods-***@lists.electorama.com
[mailto:election-methods-***@lists.electorama.com] On Behalf Of Dave
Ketchum
Sent: Thursday, July 02, 2009 4:04 PM
To: Raph Frank
Cc: EM
Subject: Re: [EM] National Popular Vote & Condorcet
On Wed, Jul 1, 2009 at 10:34 PM, Dave
Approval data - needs thought but my initial thought is as if each
approval was a plurality vote - does mean a voter approving 2 gets 2 votes
counted but relative counts per candidate comes out ok.
IRV or Range - examples of methods that should be avoided by states
willing to have their data included - unless they are willing and able to
convert to a method that is supported.
To summarize my thinking:

Each state controls how it interacts with its voters - so let them
choose their own way, such that their voters' desires get properly
added into the national X*X array.
I would group them as
A vote for candidate A is considered
A>(others)
This reads as giving the same power as if ranking ONE candidate in
Condorcet - simple and declarably accurate.
Matrix is provided directly
Here the voters could have ranked exactly as in Condorcet, but
standard IRV counting does not extract all that the voters say. I
would leave it to the state - perhaps they will do an X*X matrix. I
do not like what I read below - better for such states to avoid such
as IRV when they do not fit with what is reasonably the standard.
Summary: Presumably this state does IRV for races it controls. It's
voters, and those thinking in other states, would like something other
than what follows for this race in this state.
Extract as much info as possible, for example
A: 100
B: 82
C: 41
D: 13
100: A>(others)
82: B>(others)
41: C>(others)
13: D>(others)
D elliminated
4 go to A
3 go to B
5 go to C
1 untransferable
Votes are now
100: A>(others)
82: B>(others)
41: C>(others)
4: D>A>(others)
3: D>B>(others)
5: D>C>(others)
1: D (so effectively D>(others)
C would then be eliminated and we would get info about 2nd choices for
C. One issue here is that C>D>A would not be distinguished from C>A
(as both would transfer to A).
Approval/Range
For approval my first thought is that they are presumably doing
approval and my first choice for them is whatever Condorcet states do
when their voters vote with approval thinking.

For Range the thinking is much as I do above for IRV.
This are somewhat different versions of the same method. There isn't
any way to reverse the process back to votes.
You give each candidate a plurality vote of (votes obtained)*[votes
cast/total approval]. This would at least mean that the state
wouldn't be over represented.
If there were 1000 votes cast and the results were
A: 800
B: 400
C: 300
Total 1500
A: 800/1.5 = 533
B: 400/1.5 = 267
C: 300/1.5 = 200
I you assume that voters will use the strategy of vote for their
favourite of the top-2 and all they prefer to the expected winner, you
could estimate the preference table.
It is possible to find a matrix that matches the approval results, but
there wouldn't be a unique one.
"Add" A's 800 approvals
800: A
"Add" B's 400 approvals
480: A
320: A+B
200 split into
80: B
Total
480: A
320: A+B
80: B
and so on.
That would result in an assumption that lots of votes cast blank votes.
Another option would be to find the "top-2". This could be the 2 most
approved candidates, W (winner) and S (second).
It is assumed that W and S voters would not approve each other to the
greatest extend possible.
So, the above example becomes
A: 800
B: 400
C: 300
Total 1500
A and B are top-2, if 800 approved A and 400 approved B, then at least
200 must have approved both. This assumes
600: A
200: A+B
200: B
This means that every voter is assumed to approve one of the top-2.
The rest of the candidates could then be assumed to be random.
The full process would be
1) Assume all ballots are blank
2) Process Candidates from most to least approved
3) If any ballots are blank, then designate them as approving the
current candidate
4) Distribute any remaining approval for the candidate randomly
5) Goto 2
This gets you a set of approval ballots which is consistant with the
results. Also, it is likely to be reasonably accurate, based on the
assumption that each voter only approves one of the top-2.
It can be gamed if a party runs 2 candidates, as then every voter is
considered to vote for one of their candidates.
One option would be to fill blank ballots and then ballots approved by
all the other candidates (bar the most approved).
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Jonathan Lundell
2009-07-02 21:43:22 UTC
Permalink
Post by Paul Kislanko
Without going into detail, if all states do not use the same
collection
method, applying a national counting method that isn't the "lowest common
denominator" method, there would be a violation of the "equal process"
clause of the 14th Amendment. In order to use a ranked-ballot
method, every
state would have to provide ranked BALLOTS to be counted.
What we have now is we can "roll up" from precinct to district to state to
national only SUMS, because everybody counts ballots the same way. If state
X counts ballots differently than state Y, we can't just "add" X and Y in
the national total without running afoul of the 14th Amendment.
Even though "I am not a lawyer", I know some who would bring that up.
The attraction of NPV, in large part (it seems to me) is its
simplicity. A simple unilateral action on the part of enough states
yields precisely a national plurality election for president, neatly
making the Electoral College a dead letter, without the need for a
constitutional amendment. (Ignoring the possibility of a challenge to
NPV on state compact grounds, or whatever--I think the language could
have been written a little better so as to avoid the appearance of a
compact, but them I'm not a lawyer either.)

NPV is making slow enough progress as it is that I can't imagine that
a competing (more complex) proposal would have any chance at all.

And (sadly, in my view) a straightforward constitutional amendment to
establish direct presidential election by any means other than
plurality would be doomed to failure by IRV vs Condorcet vs range vs
approval infighting. So it's not as if there's another path that would
get us something better than NPV. In my opinion.

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Dave Ketchum
2009-07-02 22:43:43 UTC
Permalink
Ok, I thought, and still feel, that the topic needed some airing.

With the EC, and without NPV, each state can do their own thing for
deciding what instruction to give their EC members - and could do
better than Plurality if they choose.

With NPV there is need for more thought:
Make all do Plurality? Simple. but more and more realize that
voters need more control - and there is need for recognizing that this
is a national election with more variety of voter opinions as they
prepare to vote.
Make all do an agreed better method, such as Condorcet? Worth
thought - likely needs a C. Amendment.
Each state select from an agreed set of methods? Worth thought,
but this could inspire 14th Amendment complaints.

Dave Ketchum
Post by Jonathan Lundell
Post by Paul Kislanko
Without going into detail, if all states do not use the same
collection
method, applying a national counting method that isn't the "lowest common
denominator" method, there would be a violation of the "equal
process"
clause of the 14th Amendment. In order to use a ranked-ballot
method, every
state would have to provide ranked BALLOTS to be counted.
What we have now is we can "roll up" from precinct to district to state to
national only SUMS, because everybody counts ballots the same way. If state
X counts ballots differently than state Y, we can't just "add" X and Y in
the national total without running afoul of the 14th Amendment.
Even though "I am not a lawyer", I know some who would bring that up.
The attraction of NPV, in large part (it seems to me) is its
simplicity. A simple unilateral action on the part of enough states
yields precisely a national plurality election for president, neatly
making the Electoral College a dead letter, without the need for a
constitutional amendment. (Ignoring the possibility of a challenge
to NPV on state compact grounds, or whatever--I think the language
could have been written a little better so as to avoid the
appearance of a compact, but them I'm not a lawyer either.)
NPV is making slow enough progress as it is that I can't imagine
that a competing (more complex) proposal would have any chance at all.
And (sadly, in my view) a straightforward constitutional amendment
to establish direct presidential election by any means other than
plurality would be doomed to failure by IRV vs Condorcet vs range vs
approval infighting. So it's not as if there's another path that
would get us something better than NPV. In my opinion.
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Raph Frank
2009-07-02 23:51:13 UTC
Permalink
Each state controls how it interacts with its voters - so let them choose
their own way, such that their voters' desires get properly added into the
national X*X array.
This depends, there needs to be rules on what states can do.

For example, they could create the array so that it is

State winner>(others)

for all voters in the state.

In effect, this returns things to the current, pre-NPV, system.
Post by Raph Frank
A vote for candidate A is considered
A>(others)
This reads as giving the same power as if ranking ONE candidate in Condorcet
- simple and declarably accurate.
It also means that only the expected national top-2 can get votes from
this state.

Ofc, this isn't as extreme as currently, and if other states support
more open methods, at least candidates can gain publicity in one
election for a challenge on the next.
Post by Raph Frank
Matrix is provided directly
Here the voters could have ranked exactly as in Condorcet, but standard IRV
counting does not extract all that the voters say.  I would leave it to the
state - perhaps they will do an X*X matrix.  I do not like what I read below
- better for such states to avoid such as IRV when  they do not fit with
what is reasonably the standard.
Right, if they collect ranked ballots, it would be best if they
publish the full results.

However you need to somehow handle the case where states use IRV.

For example, the State might have a rule that all EC votes for the
State are assigned to the IRV winner in the state, so they don't
publish ballot info.
Post by Raph Frank
Approval/Range
For approval my first thought is that they are presumably doing approval and
my first choice for them is whatever Condorcet states do when their voters
vote with approval thinking.
Again, the States may not publish the date required.

I would agree that a voter who approved candidate A and B should
ideally be considered

A=B>(others).

However, you can't extract that info from the approval results.
For Range the thinking is much as I do above for IRV.
Again, if the full ballot info is released, it would be worth
converting the range votes into condorcet, but there is a need to
handle things if the State doesn't provide the info.

It occurs to me that you could just include rules for comparisons
rather than trying to work out the votes for approval.

Approval

A: 800
B: 400
C: 300
Total 1500

Comparing A and B
800-400

This means that the votes are assumed to be
200: A=B
600: A>B
200: B

A>B: 600-200

Comparing B and C
400-300

B>C: 400-300

Comparing A and C
100: A=C
700: A
200: C

A>C: 700-200

Thus the rule when determining the pairwise comparisons is to assume
that the number of equality votes are minimum.

This may not even effect the result depending on completion method used.

For example:

A: 800
C: 300

must be
A=C: X
A: 800-X
B: 300-X

Thus the win margin is (800-X) - (300-X) = 500. As long as the win
margin is all that matters we can determine the exact national result
without knowing exactly the number of ballots where there is a tie.

Thus, approval, condorcet (if matrix is provided) and plurality
results can be converted to an exact matrix (or equivalent).

IRV cannot be fully supported, and ballot info is lost.
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Dave Ketchum
2009-07-03 01:46:09 UTC
Permalink
I have two basic assumptions:
States are willing to have a reasonable national count.
But some may not be willing to all go where I wish them to be -
letting their voters vote in Condorcet.

Still, some methods such as Range do not provide suitable information
for this purpose - my real goal for these is to have them use a
different, more compatible, method.

For example, a state could use Plurality for this race, whatever they
may choose to use in other races.
On Thu, Jul 2, 2009 at 10:03 PM, Dave
Each state controls how it interacts with its voters - so let them choose
their own way, such that their voters' desires get properly added into the
national X*X array.
This depends, there needs to be rules on what states can do.
For example, they could create the array so that it is
State winner>(others)
for all voters in the state.
I assume more cooperation than this.
In effect, this returns things to the current, pre-NPV, system.
Post by Raph Frank
A vote for candidate A is considered
A>(others)
This reads as giving the same power as if ranking ONE candidate in Condorcet
- simple and declarably accurate.
It also means that only the expected national top-2 can get votes from
this state.
No, for EACH candidate gets treated as A in its turn.
Ofc, this isn't as extreme as currently, and if other states support
more open methods, at least candidates can gain publicity in one
election for a challenge on the next.
Post by Raph Frank
Matrix is provided directly
Here the voters could have ranked exactly as in Condorcet, but standard IRV
counting does not extract all that the voters say. I would leave
it to the
state - perhaps they will do an X*X matrix. I do not like what I
read below
- better for such states to avoid such as IRV when they do not fit
with
what is reasonably the standard.
Right, if they collect ranked ballots, it would be best if they
publish the full results.
Since their voters are doing ranking, just as in Condorcet, they have
all the information to do an X*X array - but I avoid demanding that
they do such.
However you need to somehow handle the case where states use IRV.
For example, the State might have a rule that all EC votes for the
State are assigned to the IRV winner in the state, so they don't
publish ballot info.
The goal here is maximum practical cooperation - which includes their
EC votes getting based on the NPV winner - what I am trying for is
maximum validity for the NPV.
Post by Raph Frank
Approval/Range
For approval my first thought is that they are presumably doing approval and
my first choice for them is whatever Condorcet states do when their voters
vote with approval thinking.
Again, the States may not publish the date required.
I would agree that a voter who approved candidate A and B should
ideally be considered
A=B>(others).
However, you can't extract that info from the approval results.
For Range the thinking is much as I do above for IRV.
Again, if the full ballot info is released, it would be worth
converting the range votes into condorcet, but there is a need to
handle things if the State doesn't provide the info.
I think it best for the state to do the conversion, assuming they
insist on using a method for this race that requires painful
conversion - and, at that point, I prefer that that state have the
pain of converting.
It occurs to me that you could just include rules for comparisons
rather than trying to work out the votes for approval.
Approval
A: 800
B: 400
C: 300
Total 1500
Comparing A and B
800-400
This means that the votes are assumed to be
200: A=B
600: A>B
200: B
A>B: 600-200
Comparing B and C
400-300
B>C: 400-300
Comparing A and C
100: A=C
700: A
200: C
A>C: 700-200
Thus the rule when determining the pairwise comparisons is to assume
that the number of equality votes are minimum.
This may not even effect the result depending on completion method used.
A: 800
C: 300
must be
A=C: X
A: 800-X
B: 300-X
Thus the win margin is (800-X) - (300-X) = 500. As long as the win
margin is all that matters we can determine the exact national result
without knowing exactly the number of ballots where there is a tie.
What follows puzzles. Thinking:
Approval can easily be restated in Condorcet.
Condorcet is my intended goal, so the state has info for an X*X
array.
Plurality I say to treat as if each of those votes was Condorcet
ranking a single candidate.
For IRV the ballots contained ranking but I leave open whether
the state chooses to see all that the ballots say.
Thus, approval, condorcet (if matrix is provided) and plurality
results can be converted to an exact matrix (or equivalent).
IRV cannot be fully supported, and ballot info is lost.
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Raph Frank
2009-07-04 20:08:00 UTC
Permalink
Post by Dave Ketchum
I assume more cooperation than this.
I think we are talking "orthogonally".

The NPV plan is that some of the States enter into a compact, and then
they vote their EC votes as a single unit.

You can reasonably assume that the compact States will conform to an
agreed way of announcing their results. However, you can't assume
that non-compact States will be helpful.

One option is to just exclude non-compact States from participating,
so they either join the compact or they no longer influence who wins
the Presidency.

A more reasonable option is that you make an attempt to incorporate
the votes from the other States.

You could say that any State who won't provide a condorcet matrix of
its results in some form is excluded from the final tally. Is that
what you are proposing?

Personally, I think it would be better if the compact just had rules
for conversion into a matrix from a reasonable set of voting methods.
This also allows the States in the compact to use different methods.
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Dave Ketchum
2009-07-05 03:45:38 UTC
Permalink
Each State shall appoint, in such Manner as the Legislature thereof
may direct, a Number of Electors, equal to the whole Number of
Senators and Representatives to which the State may be entitled in
So, the states get to provide their electors, however they choose, and
the electors vote as the Electoral College.

What states generally have done is to see to slates of electors
getting nominated, and voters approving one such slate. The compact
is to see to it that the states will see to electors voting for the
whoever wins the popular vote.

Seems like they have been assuming the popular vote will be done via
Plurality - such that the national counting will be simple sums.

For the same reasons that we argue against using Plurality elsewhere,
I argue for using Condorcet here.
On Fri, Jul 3, 2009 at 2:46 AM, Dave
Post by Dave Ketchum
I assume more cooperation than this.
I think we are talking "orthogonally".
The NPV plan is that some of the States enter into a compact, and then
they vote their EC votes as a single unit.
You can reasonably assume that the compact States will conform to an
agreed way of announcing their results. However, you can't assume
that non-compact States will be helpful.
One option is to just exclude non-compact States from participating,
so they either join the compact or they no longer influence who wins
the Presidency.
There are two topics:
If they cooperate as to voting their votes get counted, for the
compact wants to be convincingly legitimate. States should want to
cooperate on this because it becomes their only path toward helping
control who gets elected.
It matters not whether they join the compact - provided it has
enough electors controlled.
A more reasonable option is that you make an attempt to incorporate
the votes from the other States.
You could say that any State who won't provide a condorcet matrix of
its results in some form is excluded from the final tally. Is that
what you are proposing?
Not quite, for there is a reasonable conversion from Plurality. For
other methods the basic desire is for the state to make a better
choice of method - or get punished by there being no reasonable
substitute.
Personally, I think it would be better if the compact just had rules
for conversion into a matrix from a reasonable set of voting methods.
This also allows the States in the compact to use different methods.
My reading is that the compact was assuming voting was done via
Plurality - it needing nothing about voting method.

I would like to start with enough states doing Plurality plus, perhaps
a few doing Condorcet, to encourage others to do Condorcet. I can
hope states thinking of IRV or Range can be convinced to join in.
Specifically for IRV, while the voting is ranked, the method does not
include counting suitable for my purpose - anyway, let such states
cooperate a bit. For Range there can be some debating as to method,
but the hoped for result is to be rid of Range for this race.

Markus Schulze
2009-07-01 12:27:10 UTC
Permalink
Hallo,

this problem had already been mentioned here:

http://article.gmane.org/gmane.politics.election-methods/10991

Markus Schulze


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