The rationale under the "winning votes" defeat strength measure
Hello,
I have a question regarding defeat strength measures. I observed that most
voting rules researchers prefer the "winning votes" (WV) measure to
"margins". In particular, to my knowledge, all real-life implementations of
Schulze use this measure. Since I'm thinking of engaging in promoting
Condorcet methods in my country, I'd like to better understand the
arguments behind this opinion. In particular:
-
What exactly are the axioms that Condorcet rules with WV satisfy, but
with margins do not? (I'm only aware of the Plurality criterion) -
I have sometimes read that WV are better to prevent strategic behavior
of the voters (without much details), but do you have any idea how to
justify WV more "intuitively" or "philosophically", assuming sincere votes?
Margins are very easy to justify. I came up with two
possible justifications for WV here (described below), but I'm not sure how
convincing they could be for the general audience. -
Don't you think it is "ugly" that the WV measure applied e.g., to
Schulze or RP/MAM requires us to artificially exclude "50% vs. 50%" ties
between candidates from consideration (or equivalently, to mark them as the
weakest) --- and that a victory "50%+1 vs. 50%-1" is rapidly considered to
be quite strong, stronger than e.g., a "45% vs. 1%" victory (with 54%
voters who rank both candidates equally)? Under margins, ties or close ties
are naturally considered the weakest. How would you refute this argument?
Regarding pt. 2, here are my ideas for a high-level intuitive principle
behind WV:
(1) "It is much harder (infinitely harder?) to convince a voter to change
his mind from B<A to A>B, than it is to change his mind from A=B to A>B".
Then, in particular, it is more probable that a "45% vs. 1%" victory would
become a "45% vs. 55%" defeat, than that a "51% vs. 49%" victory would
become a defeat.
(2) "If a voter votes for A=B, then he is not neutral, but he is actively
voting against treating the resolution of the matchup between A and B as
important". Then, in particular, in the case of a "45% vs. 1%" victory, we
in fact have 45% of voters who consider it important to resolve the matchup
in a particular direction, and 55% of voters who think otherwise. This is a
smaller number than for a "51% vs. 49%" victory.
Curious to hear your ideas.
Best,
Grzegorz
Hi Grzegorz,
- What exactly are the axioms that Condorcet rules with WV satisfy, but with
margins do not? (I'm only aware of the Plurality criterion)
Very few have been articulated, but:
- I have sometimes read that WV are better to prevent strategic behavior of
the voters (without much details),
I do use the minimal defense criterion, which represents the notion that a full
majority of voters can always get their way if they want to, so it will reduce
compromise strategy for the majority if you just give them their way when you
know what it is.
To me, WV resolution is an approximation of an ideal. I made a webpage that
attempts to show what options are available for electing from a provided cycle,
with the aim of avoiding compromise incentive when you can:
https://votingmethods.net/check
This doesn't always favor WV, and sometimes there are no actual solutions.
but do you have any idea how to justify WV
more "intuitively" or "philosophically", assuming sincere votes? Margins are
very easy to justify. I came up with two possible justifications for WV here
(described below), but I'm not sure how convincing they could be for the
general audience.
Here I'm not sure. I guess by "sincere votes" you mean that absence of a
pairwise preference indicates an expression that two candidates are equal. Or
maybe that truncation is not different from explicit equal ranking.
- Don't you think it is "ugly" that the WV measure applied e.g., to Schulze
or RP/MAM requires us to artificially exclude "50% vs. 50%" ties between
candidates from consideration (or equivalently, to mark them as the weakest)
That's never occurred to me actually. All non-wins are excluded from
consideration.
--- and that a victory "50%+1 vs. 50%-1" is rapidly considered to be quite
strong, stronger than e.g., a "45% vs. 1%" victory (with 54% voters who rank
both candidates equally)? Under margins, ties or close ties are naturally
considered the weakest. How would you refute this argument?
Ideally by some kind of rephrasing. I don't know if this is possible, but it
would be nice if the matter could be presented without making it feel like the
defeats themselves have an interest in being respected.
Alternatively, you want to find a explanation where losing votes are just
meaningless, because for the practical purposes (the strategic incentive ones),
they are. You don't obtain a valid complaint against the method by losing a
close race, you can only get one by winning races and losing anyway because you
didn't lie.
(In a 51:49 matchup, those on the losing side have no power to lie and change
the outcome (we hope), while there is considerable possibility that those on the
51 side could lie and win (i.e. if they had not), because they comprise more
than half the voters. With 45:1, there are decent odds that those on the 45%
side could win by lying; your method could determine this to be sure, if you
wanted, before ruling for instance that 45:1 prevails over a win of 40:39. WV is
just making a mathematically easy "best guess.")
Regarding pt. 2, here are my ideas for a high-level intuitive principle behind
WV:
(1) "It is much harder (infinitely harder?) to convince a voter to change his
mind from B<A to A>B, than it is to change his mind from A=B to A>B". Then, in
particular, it is more probable that a "45% vs. 1%" victory would become a
"45% vs. 55%" defeat, than that a "51% vs. 49%" victory would become a defeat.
That has some familiarity to me. If the winning side has a full majority then we
"know" it is right. In fact if you entertain the concept of an overall "median
voter" it suggests to us something about what that voter thinks.
Though I understand that you want to suppose that the equalities are in fact
sincere.
In that case, if it's 45% A>B, 54% A=B, 1% B>A, my observation would be that the
median position is that A and B are equal. The 54% aren't just abstaining, are
they? I don't think that's what the assumption of sincerity implies.
Your second idea is kind of suggestive of this actually... You're just focusing
more on voters' desire for how the matchup is handled.
(2) "If a voter votes for A=B, then he is not neutral, but he is actively
voting against treating the resolution of the matchup between A and B as
important". Then, in particular, in the case of a "45% vs. 1%" victory, we in
fact have 45% of voters who consider it important to resolve the matchup in a
particular direction, and 55% of voters who think otherwise. This is a smaller
number than for a "51% vs. 49%" victory.
I view this possibility of voters having such a sentiment, and acting on it in
this way, more as something useful that WV enables. I don't think we can say
it's intuitively the case that voters are meaning to do this.
Kevin
votingmethods.net
The way I've always seen it is that margins makes more sense from a purely philosophical or mathematical point of view. As Grzegorz alluded to, winning votes can lead to weird discontinuities, and having 50-0 as a "smaller" win than 51-49 seems weird, to say the least. I see winning votes as purely practical and pragmatic. It purely exists because of real-life strategic concerns, not because of any philosophical or mathematical ideal. It's clunky, ugly, and mathematically illogical, but seems to deal with certain situations better than margins.
Toby
On Wednesday 25 June 2025 at 17:25:09 BST, Kevin Venzke via Election-Methods election-methods@lists.electorama.com wrote:
Hi Grzegorz,
- What exactly are the axioms that Condorcet rules with WV satisfy, but with
margins do not? (I'm only aware of the Plurality criterion)
Very few have been articulated, but:
- I have sometimes read that WV are better to prevent strategic behavior of
the voters (without much details),
I do use the minimal defense criterion, which represents the notion that a full
majority of voters can always get their way if they want to, so it will reduce
compromise strategy for the majority if you just give them their way when you
know what it is.
To me, WV resolution is an approximation of an ideal. I made a webpage that
attempts to show what options are available for electing from a provided cycle,
with the aim of avoiding compromise incentive when you can:
https://votingmethods.net/check
This doesn't always favor WV, and sometimes there are no actual solutions.
but do you have any idea how to justify WV
more "intuitively" or "philosophically", assuming sincere votes? Margins are
very easy to justify. I came up with two possible justifications for WV here
(described below), but I'm not sure how convincing they could be for the
general audience.
Here I'm not sure. I guess by "sincere votes" you mean that absence of a
pairwise preference indicates an expression that two candidates are equal. Or
maybe that truncation is not different from explicit equal ranking.
- Don't you think it is "ugly" that the WV measure applied e.g., to Schulze
or RP/MAM requires us to artificially exclude "50% vs. 50%" ties between
candidates from consideration (or equivalently, to mark them as the weakest)
That's never occurred to me actually. All non-wins are excluded from
consideration.
--- and that a victory "50%+1 vs. 50%-1" is rapidly considered to be quite
strong, stronger than e.g., a "45% vs. 1%" victory (with 54% voters who rank
both candidates equally)? Under margins, ties or close ties are naturally
considered the weakest. How would you refute this argument?
Ideally by some kind of rephrasing. I don't know if this is possible, but it
would be nice if the matter could be presented without making it feel like the
defeats themselves have an interest in being respected.
Alternatively, you want to find a explanation where losing votes are just
meaningless, because for the practical purposes (the strategic incentive ones),
they are. You don't obtain a valid complaint against the method by losing a
close race, you can only get one by winning races and losing anyway because you
didn't lie.
(In a 51:49 matchup, those on the losing side have no power to lie and change
the outcome (we hope), while there is considerable possibility that those on the
51 side could lie and win (i.e. if they had not), because they comprise more
than half the voters. With 45:1, there are decent odds that those on the 45%
side could win by lying; your method could determine this to be sure, if you
wanted, before ruling for instance that 45:1 prevails over a win of 40:39. WV is
just making a mathematically easy "best guess.")
Regarding pt. 2, here are my ideas for a high-level intuitive principle behind
WV:
(1) "It is much harder (infinitely harder?) to convince a voter to change his
mind from B<A to A>B, than it is to change his mind from A=B to A>B". Then, in
particular, it is more probable that a "45% vs. 1%" victory would become a
"45% vs. 55%" defeat, than that a "51% vs. 49%" victory would become a defeat.
That has some familiarity to me. If the winning side has a full majority then we
"know" it is right. In fact if you entertain the concept of an overall "median
voter" it suggests to us something about what that voter thinks.
Though I understand that you want to suppose that the equalities are in fact
sincere.
In that case, if it's 45% A>B, 54% A=B, 1% B>A, my observation would be that the
median position is that A and B are equal. The 54% aren't just abstaining, are
they? I don't think that's what the assumption of sincerity implies.
Your second idea is kind of suggestive of this actually... You're just focusing
more on voters' desire for how the matchup is handled.
(2) "If a voter votes for A=B, then he is not neutral, but he is actively
voting against treating the resolution of the matchup between A and B as
important". Then, in particular, in the case of a "45% vs. 1%" victory, we in
fact have 45% of voters who consider it important to resolve the matchup in a
particular direction, and 55% of voters who think otherwise. This is a smaller
number than for a "51% vs. 49%" victory.
I view this possibility of voters having such a sentiment, and acting on it in
this way, more as something useful that WV enables. I don't think we can say
it's intuitively the case that voters are meaning to do this.
Kevin
votingmethods.net
Election-Methods mailing list - see https://electorama.com/em for list info
Hi Toby,
Le mercredi 25 juin 2025 à 12:02:55 UTC−5, Toby Pereira via Election-Methods election-methods@lists.electorama.com a écrit :
The way I've always seen it is that margins makes more sense from a purely philosophical or mathematical point of
view. As Grzegorz alluded to, winning votes can lead to weird discontinuities, and having 50-0 as a "smaller" win
than 51-49 seems weird, to say the least. I see winning votes as purely practical and pragmatic. It purely exists
because of real-life strategic concerns, not because of any philosophical or mathematical ideal. It's clunky, ugly, and
mathematically illogical, but seems to deal with certain situations better than margins.
For me, I note that when someone comes up with a new method off the top of their
head and posts it to the EM list, it's quite frequent that these methods give
results that are similar to WV results. These may not even be Condorcet methods.
This suggests to me that WV's results, at least, are not very unique or
arbitrary. It's still possible to feel that there's an ugliness to how it
gets to the outcome, of course.
Kevin
votingmethods.net
-
You could say that the philosophy of margins is to give good results with sincere votes.
-
But how about coping with strategic voting?
-
The main argument is maybe that in large public real life Condorcet elections it is very difficult to implement and coordinate successful malicious strategies, and therefore one should expect rational voters to vote sincerely.
-
You could say that winning votes are intended to cope with threats of some insincere voting scenarios.
-
But how about electing the best candidate when votes are sincere?
-
A good argument might be that usually there is a Condorcet winner anyway, and if not, most voters tend to rank all major candidates anyway, which makes strange results less likely. Vote truncation for strategic or defensive reasons might be rare. One should also encourage voters not to truncate since we want to get all their preferences, to be able to pick the best winner.
Juho
On 25. Jun 2025, at 20.02, Toby Pereira via Election-Methods election-methods@lists.electorama.com wrote:
The way I've always seen it is that margins makes more sense from a purely philosophical or mathematical point of view. As Grzegorz alluded to, winning votes can lead to weird discontinuities, and having 50-0 as a "smaller" win than 51-49 seems weird, to say the least. I see winning votes as purely practical and pragmatic. It purely exists because of real-life strategic concerns, not because of any philosophical or mathematical ideal. It's clunky, ugly, and mathematically illogical, but seems to deal with certain situations better than margins.
Toby
On Wednesday 25 June 2025 at 17:25:09 BST, Kevin Venzke via Election-Methods election-methods@lists.electorama.com wrote:
Hi Grzegorz,
- What exactly are the axioms that Condorcet rules with WV satisfy, but with
margins do not? (I'm only aware of the Plurality criterion)
Very few have been articulated, but:
- I have sometimes read that WV are better to prevent strategic behavior of
the voters (without much details),
I do use the minimal defense criterion, which represents the notion that a full
majority of voters can always get their way if they want to, so it will reduce
compromise strategy for the majority if you just give them their way when you
know what it is.
To me, WV resolution is an approximation of an ideal. I made a webpage that
attempts to show what options are available for electing from a provided cycle,
with the aim of avoiding compromise incentive when you can:
https://votingmethods.net/check
This doesn't always favor WV, and sometimes there are no actual solutions.
but do you have any idea how to justify WV
more "intuitively" or "philosophically", assuming sincere votes? Margins are
very easy to justify. I came up with two possible justifications for WV here
(described below), but I'm not sure how convincing they could be for the
general audience.
Here I'm not sure. I guess by "sincere votes" you mean that absence of a
pairwise preference indicates an expression that two candidates are equal. Or
maybe that truncation is not different from explicit equal ranking.
- Don't you think it is "ugly" that the WV measure applied e.g., to Schulze
or RP/MAM requires us to artificially exclude "50% vs. 50%" ties between
candidates from consideration (or equivalently, to mark them as the weakest)
That's never occurred to me actually. All non-wins are excluded from
consideration.
--- and that a victory "50%+1 vs. 50%-1" is rapidly considered to be quite
strong, stronger than e.g., a "45% vs. 1%" victory (with 54% voters who rank
both candidates equally)? Under margins, ties or close ties are naturally
considered the weakest. How would you refute this argument?
Ideally by some kind of rephrasing. I don't know if this is possible, but it
would be nice if the matter could be presented without making it feel like the
defeats themselves have an interest in being respected.
Alternatively, you want to find a explanation where losing votes are just
meaningless, because for the practical purposes (the strategic incentive ones),
they are. You don't obtain a valid complaint against the method by losing a
close race, you can only get one by winning races and losing anyway because you
didn't lie.
(In a 51:49 matchup, those on the losing side have no power to lie and change
the outcome (we hope), while there is considerable possibility that those on the
51 side could lie and win (i.e. if they had not), because they comprise more
than half the voters. With 45:1, there are decent odds that those on the 45%
side could win by lying; your method could determine this to be sure, if you
wanted, before ruling for instance that 45:1 prevails over a win of 40:39. WV is
just making a mathematically easy "best guess.")
Regarding pt. 2, here are my ideas for a high-level intuitive principle behind
WV:
(1) "It is much harder (infinitely harder?) to convince a voter to change his
mind from B<A to A>B, than it is to change his mind from A=B to A>B". Then, in
particular, it is more probable that a "45% vs. 1%" victory would become a
"45% vs. 55%" defeat, than that a "51% vs. 49%" victory would become a defeat.
That has some familiarity to me. If the winning side has a full majority then we
"know" it is right. In fact if you entertain the concept of an overall "median
voter" it suggests to us something about what that voter thinks.
Though I understand that you want to suppose that the equalities are in fact
sincere.
In that case, if it's 45% A>B, 54% A=B, 1% B>A, my observation would be that the
median position is that A and B are equal. The 54% aren't just abstaining, are
they? I don't think that's what the assumption of sincerity implies.
Your second idea is kind of suggestive of this actually... You're just focusing
more on voters' desire for how the matchup is handled.
(2) "If a voter votes for A=B, then he is not neutral, but he is actively
voting against treating the resolution of the matchup between A and B as
important". Then, in particular, in the case of a "45% vs. 1%" victory, we in
fact have 45% of voters who consider it important to resolve the matchup in a
particular direction, and 55% of voters who think otherwise. This is a smaller
number than for a "51% vs. 49%" victory.
I view this possibility of voters having such a sentiment, and acting on it in
this way, more as something useful that WV enables. I don't think we can say
it's intuitively the case that voters are meaning to do this.
Kevin
votingmethods.net
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list info
There is also the Non-Drastic Defense criterion, which says that if more
than half the voters vote X above Y and X no lower than equal-top then
Y can't win.
46 A>C (maybe sincere is A or A>B)
17 B
17 B>C
20 C=B (maybe sincere is C>B)
B>A 54-46, A>C 63-37, C>B 46-34.
Here B is above A and no lower than equal-top on more than half the
ballots, but Margins elects A. Winning Votes elects B.
Also Margins can fail Later-no-Help especially egregiously and elect the
weakest candidate:
46 A
44 B>C (sincere might be B or B>A)
10 C
Margins elects B (failing the Plurality criterion). How does the B
voters ranking C remotely justify switching the win from A to B?? A
pairwise beats and positionally dominates B, and C is ranked above
bottom on the most number of ballots. I can't accept any method that
elects B here. (Or A in the previous example.)
I have long since decided that resolving Condorcet top cycles by
deciding (on some basis or another) that some pairwise defeats are
"weaker" than others is a dead end. I vastly prefer 3 other Condorcet
methods: Margins Sorted Approval(explicit), Margins Sorted Approval
(implicit), and "Benham".
They all resist Burial better than Margins or Winning Votes, and Margins
Sorted Approval is very elegant.
Chris Benham
On 26/06/2025 1:50 am, Kevin Venzke via Election-Methods wrote:
Hi Grzegorz,
- What exactly are the axioms that Condorcet rules with WV satisfy, but with
margins do not? (I'm only aware of the Plurality criterion)
Very few have been articulated, but:
- I have sometimes read that WV are better to prevent strategic behavior of
the voters (without much details),
I do use the minimal defense criterion, which represents the notion that a full
majority of voters can always get their way if they want to, so it will reduce
compromise strategy for the majority if you just give them their way when you
know what it is.
To me, WV resolution is an approximation of an ideal. I made a webpage that
attempts to show what options are available for electing from a provided cycle,
with the aim of avoiding compromise incentive when you can:
https://votingmethods.net/check
This doesn't always favor WV, and sometimes there are no actual solutions.
but do you have any idea how to justify WV
more "intuitively" or "philosophically", assuming sincere votes? Margins are
very easy to justify. I came up with two possible justifications for WV here
(described below), but I'm not sure how convincing they could be for the
general audience.
Here I'm not sure. I guess by "sincere votes" you mean that absence of a
pairwise preference indicates an expression that two candidates are equal. Or
maybe that truncation is not different from explicit equal ranking.
- Don't you think it is "ugly" that the WV measure applied e.g., to Schulze
or RP/MAM requires us to artificially exclude "50% vs. 50%" ties between
candidates from consideration (or equivalently, to mark them as the weakest)
That's never occurred to me actually. All non-wins are excluded from
consideration.
--- and that a victory "50%+1 vs. 50%-1" is rapidly considered to be quite
strong, stronger than e.g., a "45% vs. 1%" victory (with 54% voters who rank
both candidates equally)? Under margins, ties or close ties are naturally
considered the weakest. How would you refute this argument?
Ideally by some kind of rephrasing. I don't know if this is possible, but it
would be nice if the matter could be presented without making it feel like the
defeats themselves have an interest in being respected.
Alternatively, you want to find a explanation where losing votes are just
meaningless, because for the practical purposes (the strategic incentive ones),
they are. You don't obtain a valid complaint against the method by losing a
close race, you can only get one by winning races and losing anyway because you
didn't lie.
(In a 51:49 matchup, those on the losing side have no power to lie and change
the outcome (we hope), while there is considerable possibility that those on the
51 side could lie and win (i.e. if they had not), because they comprise more
than half the voters. With 45:1, there are decent odds that those on the 45%
side could win by lying; your method could determine this to be sure, if you
wanted, before ruling for instance that 45:1 prevails over a win of 40:39. WV is
just making a mathematically easy "best guess.")
Regarding pt. 2, here are my ideas for a high-level intuitive principle behind
WV:
(1) "It is much harder (infinitely harder?) to convince a voter to change his
mind from B<A to A>B, than it is to change his mind from A=B to A>B". Then, in
particular, it is more probable that a "45% vs. 1%" victory would become a
"45% vs. 55%" defeat, than that a "51% vs. 49%" victory would become a defeat.
That has some familiarity to me. If the winning side has a full majority then we
"know" it is right. In fact if you entertain the concept of an overall "median
voter" it suggests to us something about what that voter thinks.
Though I understand that you want to suppose that the equalities are in fact
sincere.
In that case, if it's 45% A>B, 54% A=B, 1% B>A, my observation would be that the
median position is that A and B are equal. The 54% aren't just abstaining, are
they? I don't think that's what the assumption of sincerity implies.
Your second idea is kind of suggestive of this actually... You're just focusing
more on voters' desire for how the matchup is handled.
(2) "If a voter votes for A=B, then he is not neutral, but he is actively
voting against treating the resolution of the matchup between A and B as
important". Then, in particular, in the case of a "45% vs. 1%" victory, we in
fact have 45% of voters who consider it important to resolve the matchup in a
particular direction, and 55% of voters who think otherwise. This is a smaller
number than for a "51% vs. 49%" victory.
I view this possibility of voters having such a sentiment, and acting on it in
this way, more as something useful that WV enables. I don't think we can say
it's intuitively the case that voters are meaning to do this.
Kevin
votingmethods.net
Election-Methods mailing list - see https://electorama.com/em for list info
Hi all,
Thanks for all your comments, axioms and explanations! From what I see, the
justification of WV is indeed rather pragmatic and strategy-oriented, which
is quite a problem for me. I would really prefer to avoid answering
the question: "Why did your rule elect a bad candidate in this election?"
by saying "Well, because you might have been dishonest in some specific
way, and then this candidate wouldn't be so bad". I also agree with Juho
that "in large public real life Condorcet elections it is very difficult to
implement and coordinate successful malicious strategies".
For example, the second example of Chris rather convinces me to support
margins and oppose WV, than the other way around. Let's see:
46: A
44: B>C
10: C
WV elect C here, while margins elect B. In fact, if the above preferences
are honest, then B is clearly the best candidate, since he is the closest
to be the Condorcet winner. Electing A or (especially) C would be extremely
unstable - if just one voter changes his preference from A to B, the result
would switch to B under any Condorcet rule. Moreover, B has much broader
support than C (assuming that A's supporters are truly indifferent between
both). I really can't find a logical justification of electing C here if
the voters are honest.
On the other hand, if we assume that voters were strategic and the honest
opinion of the middle voters is B or B>A, then it means that a massive
number of voters colluded to vote strategically, in a situation where (1)
the result of the race between A and B was unpredictable before the
election and B had real chances to win anyway, (2) a lot of voters had a
fragile preference of either B=A or B=C, and such a "dirty" operation of B
could easily change their minds to (respectively) A>B and C>B. I just don't
see this happening in practice. I can agree that such a theoretical
possibility is bad, because violating strategyproofness generally is bad,
but there's nothing particularly worrisome for me here.
Best,
Grzegorz
czw., 26 cze 2025 o 05:57 Chris Benham cbenhamau@yahoo.com.au napisał(a):
There is also the Non-Drastic Defense criterion, which says that if more
than half the voters vote X above Y and X no lower than equal-top then
Y can't win.
46 A>C (maybe sincere is A or A>B)
17 B
17 B>C
20 C=B (maybe sincere is C>B)
B>A 54-46, A>C 63-37, C>B 46-34.
Here B is above A and no lower than equal-top on more than half the
ballots, but Margins elects A. Winning Votes elects B.
Also Margins can fail Later-no-Help especially egregiously and elect the
weakest candidate:
46 A
44 B>C (sincere might be B or B>A)
10 C
Margins elects B (failing the Plurality criterion). How does the B
voters ranking C remotely justify switching the win from A to B?? A
pairwise beats and positionally dominates B, and C is ranked above
bottom on the most number of ballots. I can't accept any method that
elects B here. (Or A in the previous example.)
I have long since decided that resolving Condorcet top cycles by
deciding (on some basis or another) that some pairwise defeats are
"weaker" than others is a dead end. I vastly prefer 3 other Condorcet
methods: Margins Sorted Approval(explicit), Margins Sorted Approval
(implicit), and "Benham".
They all resist Burial better than Margins or Winning Votes, and Margins
Sorted Approval is very elegant.
Chris Benham
On 26/06/2025 1:50 am, Kevin Venzke via Election-Methods wrote:
Hi Grzegorz,
- What exactly are the axioms that Condorcet rules with WV satisfy,
but with
margins do not? (I'm only aware of the Plurality criterion)
Very few have been articulated, but:
- I have sometimes read that WV are better to prevent strategic
behavior of
the voters (without much details),
I do use the minimal defense criterion, which represents the notion that
a full
majority of voters can always get their way if they want to, so it will
reduce
compromise strategy for the majority if you just give them their way
when you
know what it is.
To me, WV resolution is an approximation of an ideal. I made a webpage
that
attempts to show what options are available for electing from a provided
cycle,
with the aim of avoiding compromise incentive when you can:
https://votingmethods.net/check
This doesn't always favor WV, and sometimes there are no actual
solutions.
but do you have any idea how to justify WV
more "intuitively" or "philosophically", assuming sincere votes?
Margins are
very easy to justify. I came up with two possible justifications for WV
here
(described below), but I'm not sure how convincing they could be for the
general audience.
Here I'm not sure. I guess by "sincere votes" you mean that absence of a
pairwise preference indicates an expression that two candidates are
equal. Or
maybe that truncation is not different from explicit equal ranking.
- Don't you think it is "ugly" that the WV measure applied e.g., to
Schulze
or RP/MAM requires us to artificially exclude "50% vs. 50%" ties between
candidates from consideration (or equivalently, to mark them as the
weakest)
That's never occurred to me actually. All non-wins are excluded from
consideration.
--- and that a victory "50%+1 vs. 50%-1" is rapidly considered to be
quite
strong, stronger than e.g., a "45% vs. 1%" victory (with 54% voters who
rank
both candidates equally)? Under margins, ties or close ties are
naturally
considered the weakest. How would you refute this argument?
Ideally by some kind of rephrasing. I don't know if this is possible,
but it
would be nice if the matter could be presented without making it feel
like the
defeats themselves have an interest in being respected.
Alternatively, you want to find a explanation where losing votes are just
meaningless, because for the practical purposes (the strategic incentive
ones),
they are. You don't obtain a valid complaint against the method by
losing a
close race, you can only get one by winning races and losing anyway
because you
didn't lie.
(In a 51:49 matchup, those on the losing side have no power to lie and
change
the outcome (we hope), while there is considerable possibility that
those on the
51 side could lie and win (i.e. if they had not), because they
comprise more
than half the voters. With 45:1, there are decent odds that those on the
45%
side could win by lying; your method could determine this to be sure, if
you
wanted, before ruling for instance that 45:1 prevails over a win of
40:39. WV is
just making a mathematically easy "best guess.")
Regarding pt. 2, here are my ideas for a high-level intuitive principle
behind
WV:
(1) "It is much harder (infinitely harder?) to convince a voter to
change his
mind from B<A to A>B, than it is to change his mind from A=B to A>B".
Then, in
particular, it is more probable that a "45% vs. 1%" victory would
become a
"45% vs. 55%" defeat, than that a "51% vs. 49%" victory would become a
defeat.
That has some familiarity to me. If the winning side has a full majority
then we
"know" it is right. In fact if you entertain the concept of an overall
"median
voter" it suggests to us something about what that voter thinks.
Though I understand that you want to suppose that the equalities are in
fact
sincere.
In that case, if it's 45% A>B, 54% A=B, 1% B>A, my observation would be
that the
median position is that A and B are equal. The 54% aren't just
abstaining, are
they? I don't think that's what the assumption of sincerity implies.
Your second idea is kind of suggestive of this actually... You're just
focusing
more on voters' desire for how the matchup is handled.
(2) "If a voter votes for A=B, then he is not neutral, but he is
actively
voting against treating the resolution of the matchup between A and B as
important". Then, in particular, in the case of a "45% vs. 1%" victory,
we in
fact have 45% of voters who consider it important to resolve the
matchup in a
particular direction, and 55% of voters who think otherwise. This is a
smaller
number than for a "51% vs. 49%" victory.
I view this possibility of voters having such a sentiment, and acting on
it in
this way, more as something useful that WV enables. I don't think we can
say
it's intuitively the case that voters are meaning to do this.
Kevin
votingmethods.net
Election-Methods mailing list - see https://electorama.com/em for list
info
46: A
44: B>C
10: C
WV elect C here, while margins elect B. In fact, if the above
preferences are honest, then B is clearly the best candidate, since he
is the closest to be the Condorcet winner.
I don't see "closest to the Condorcet winner" as being necessarily
especially positive, let alone the compelling consideration. The actual
voted CW has a strong case to be elected and of course must be in a
Condorcet method. But "close to" doesn't mean anything.
Imagine you are an A supporter, or simply a sane sensible person
(preferably one who has never heard of Condorcet or Margins). Who do
you think should win this election?
46 A
44 B
10 C
Let me guess that you agree with me that the answer is A. Now let's
change that a little bit to this:
46 A
44 B>C
10 C
By what bizarre stretch of the imagination has extra (second place)
votes for C strengthened any candidate other than C ? The winner
should either still be A (the Hare and Benham winner) or change to C
(the WV and Margins Sorted Approval(implicit) and
Smith//Approval(implicit) winner).
Electing A or (especially) C would be extremely unstable - if just one
voter changes his preference from A to B, the result would switch to B
under any Condorcet rule.
I find this to be a very weak and bizarre argument. Any close election
(Condorcet or not) can be "unstable" in this way.
Moreover, B has much broader support than C (assuming that A's
supporters are truly indifferent between both).
Only C is voted above bottom on more than half the ballots. There was a
criterion suggested called something like "Possible Approval Winner"
that said that if the voters all inserted an approval cutoff in their
rankings either only approving those candidates they vote below no
others or all except those they vote below no others or anywhere in
between, then a candidate who can't possibly be the most approved
candidate can't win.
In this example the most approved candidate can only be A or C.
My favourite Condorcet method is Margins Sorted Approval (explicit):
Voters rank however many candidates they wish and also indicate an
approval threshold. Initially order the candidates according to their
approval scores. Check the pairwise result of the adjacent pair of
candidates with smallest difference in their approval scores.(If there
is a tie for this then the lowest-ordered pair among the tied pairs.) If
the lower-ordered of the two pairwise beats the higher-ordered
candidate, then those two candidates change places in the order. Repeat
this procedure to the end. The candidate at the top of the final order
is the winner.
(The "implicit" version is the same except that ranking is interpreted
as approval.)
In this example, depending on whether or not the B>C voters approve C,
the initial order (based on approval scores) is either A>B>C or
C>A>B. In neither case is any pair of adjacent candidates out of order
pairwise, i.e. in the first case A pairwise beats B and B pairwise
beats C and in the second case C pairwise beats A and A pairwise beats
B. So either way the initial order is the final order and so the
winner is either A or C.
"Benham" is the simplest and best of the Hare-Condorcet hybrids.
Voters strictly rank from the top however many candidates they wish.
Before any and each elimination we check for a pairwise-beats-all
candidate among the remaining candidates and elect the first one we
find. Until then we one-at-a-time eliminate the candidate that is the
highest voted remaining candidate on the smallest number of ballots.
(Allowing above-bottom equal ranking makes Push-over strategy easier. I
suggest interpreting ballots that have more than one candidate at the
same rank as having truncated just above that rank. I have the same
opinion about Hare.)
These methods I prefer to Winning Votes. Margins is beyond the pale. I
look forward to reading someone's argument that electing A in my other
example is justified.
46 A>C
17 B
17 B>C
20 B=C
Chris Benham
On 26/06/2025 9:12 pm, Grzegorz Pierczyński wrote:
Hi all,
Thanks for all your comments, axioms and explanations! From what I
see, the justification of WV is indeed rather pragmatic and
strategy-oriented, which is quite a problem for me. I would really
prefer to avoid answering the question: "Why did your rule elect a bad
candidate in this election?" by saying "Well, because you might have
been dishonest in some specific way, and then this candidate wouldn't
be so bad". I also agree with Juho that "in large public real life
Condorcet elections it is very difficult to implement and coordinate
successful malicious strategies".
For example, the second example of Chris rather convinces me to
support margins and oppose WV, than the other way around. Let's see:
46: A
44: B>C
10: C
WV elect C here, while margins elect B. In fact, if the above
preferences are honest, then B is clearly the best candidate, since he
is the closest to be the Condorcet winner. Electing A or (especially)
C would be extremely unstable - if just one voter changes his
preference from A to B, the result would switch to B under any
Condorcet rule. Moreover, B has much broader support than C (assuming
that A's supporters are truly indifferent between both). I really
can't find a logical justification of electing C here if the voters
are honest.
On the other hand, if we assume that voters were strategic and the
honest opinion of the middle voters is B or B>A, then it means that a
massive number of voters colluded to vote strategically, in a
situation where (1) the result of the race between A and B was
unpredictable before the election and B had real chances to win
anyway, (2) a lot of voters had a fragile preference of either B=A or
B=C, and such a "dirty" operation of B could easily change their minds
to (respectively) A>B and C>B. I just don't see this happening in
practice. I can agree that such a theoretical possibility is bad,
because violating strategyproofness generally is bad, but there's
nothing particularly worrisome for me here.
Best,
Grzegorz
czw., 26 cze 2025 o 05:57 Chris Benham cbenhamau@yahoo.com.au
napisał(a):
There is also the Non-Drastic Defense criterion, which says that
if more
than half the voters vote X above Y and X no lower than equal-top
then
Y can't win.
46 A>C (maybe sincere is A or A>B)
17 B
17 B>C
20 C=B (maybe sincere is C>B)
B>A 54-46, A>C 63-37, C>B 46-34.
Here B is above A and no lower than equal-top on more than half the
ballots, but Margins elects A. Winning Votes elects B.
Also Margins can fail Later-no-Help especially egregiously and
elect the
weakest candidate:
46 A
44 B>C (sincere might be B or B>A)
10 C
Margins elects B (failing the Plurality criterion). How does the B
voters ranking C remotely justify switching the win from A to B?? A
pairwise beats and positionally dominates B, and C is ranked above
bottom on the most number of ballots. I can't accept any method that
elects B here. (Or A in the previous example.)
I have long since decided that resolving Condorcet top cycles by
deciding (on some basis or another) that some pairwise defeats are
"weaker" than others is a dead end. I vastly prefer 3 other Condorcet
methods: Margins Sorted Approval(explicit), Margins Sorted Approval
(implicit), and "Benham".
They all resist Burial better than Margins or Winning Votes, and
Margins
Sorted Approval is very elegant.
Chris Benham
On 26/06/2025 1:50 am, Kevin Venzke via Election-Methods wrote:
Hi Grzegorz,
- What exactly are the axioms that Condorcet rules with WV
satisfy, but with
margins do not? (I'm only aware of the Plurality criterion)
Very few have been articulated, but:
- I have sometimes read that WV are better to prevent
strategic behavior of
the voters (without much details),
I do use the minimal defense criterion, which represents the
notion that a full
majority of voters can always get their way if they want to, so
it will reduce
compromise strategy for the majority if you just give them their
way when you
know what it is.
To me, WV resolution is an approximation of an ideal. I made a
webpage that
attempts to show what options are available for electing from a
provided cycle,
with the aim of avoiding compromise incentive when you can:
https://votingmethods.net/check
This doesn't always favor WV, and sometimes there are no actual
solutions.
but do you have any idea how to justify WV
more "intuitively" or "philosophically", assuming sincere
votes? Margins are
very easy to justify. I came up with two possible
justifications for WV here
(described below), but I'm not sure how convincing they could
be for the
general audience.
Here I'm not sure. I guess by "sincere votes" you mean that
absence of a
pairwise preference indicates an expression that two candidates
are equal. Or
maybe that truncation is not different from explicit equal ranking.
- Don't you think it is "ugly" that the WV measure applied
e.g., to Schulze
or RP/MAM requires us to artificially exclude "50% vs. 50%"
ties between
candidates from consideration (or equivalently, to mark them as
the weakest)
That's never occurred to me actually. All non-wins are excluded from
consideration.
--- and that a victory "50%+1 vs. 50%-1" is rapidly considered
to be quite
strong, stronger than e.g., a "45% vs. 1%" victory (with 54%
voters who rank
both candidates equally)? Under margins, ties or close ties are
naturally
considered the weakest. How would you refute this argument?
Ideally by some kind of rephrasing. I don't know if this is
possible, but it
would be nice if the matter could be presented without making it
feel like the
defeats themselves have an interest in being respected.
Alternatively, you want to find a explanation where losing votes
are just
meaningless, because for the practical purposes (the strategic
incentive ones),
they are. You don't obtain a valid complaint against the method
by losing a
close race, you can only get one by winning races and losing
anyway because you
didn't lie.
(In a 51:49 matchup, those on the losing side have no power to
lie and change
the outcome (we hope), while there is considerable possibility
that those on the
51 side could lie and win (i.e. if they had not), because they
comprise more
than half the voters. With 45:1, there are decent odds that
those on the 45%
side could win by lying; your method could determine this to be
sure, if you
wanted, before ruling for instance that 45:1 prevails over a win
of 40:39. WV is
just making a mathematically easy "best guess.")
Regarding pt. 2, here are my ideas for a high-level intuitive
principle behind
WV:
(1) "It is much harder (infinitely harder?) to convince a voter
to change his
mind from B<A to A>B, than it is to change his mind from A=B to
A>B". Then, in
particular, it is more probable that a "45% vs. 1%" victory
would become a
"45% vs. 55%" defeat, than that a "51% vs. 49%" victory would
become a defeat.
That has some familiarity to me. If the winning side has a full
majority then we
"know" it is right. In fact if you entertain the concept of an
overall "median
voter" it suggests to us something about what that voter thinks.
Though I understand that you want to suppose that the equalities
are in fact
sincere.
In that case, if it's 45% A>B, 54% A=B, 1% B>A, my observation
would be that the
median position is that A and B are equal. The 54% aren't just
abstaining, are
they? I don't think that's what the assumption of sincerity implies.
Your second idea is kind of suggestive of this actually...
You're just focusing
more on voters' desire for how the matchup is handled.
(2) "If a voter votes for A=B, then he is not neutral, but he
is actively
voting against treating the resolution of the matchup between A
and B as
important". Then, in particular, in the case of a "45% vs. 1%"
victory, we in
fact have 45% of voters who consider it important to resolve
the matchup in a
particular direction, and 55% of voters who think otherwise.
This is a smaller
number than for a "51% vs. 49%" victory.
I view this possibility of voters having such a sentiment, and
acting on it in
this way, more as something useful that WV enables. I don't
think we can say
it's intuitively the case that voters are meaning to do this.
Kevin
votingmethods.net http://votingmethods.net
Election-Methods mailing list - see https://electorama.com/em
for list info
Hi Chris,
Well, the intuition that "if there is no CW, then the candidate who was (in
some sense) the closest to be the CW should win" is a high-level rationale
behind a lot of rules (Minimax, Kemeny-Young, Dodgdon, Ranked Pairs,
Schulze, etc.) introduced by different people over time. I understand that
you don't share this intuition and prefer different methods, but it's quite
radical to call it "very weak" and "bizzarre".
"Any close election (Condorcet or not) can be "unstable" in this way."
Yes, but for me there is a difference whether the result of the closest
(least stable) comparison between A and B decides between the election of A
or B (which is natural) or between the election of B or C (which is weird).
"By what bizarre stretch of the imagination has extra (second place) votes
for C strengthened any candidate other than C? The winner should either
still be A or change to C."
You think this is bizarre because of the violation of IIA or the violation
of LNH? In both cases this is unavoidable under any Condorcet rule, so I'm
a bit surprised by this argument. Since you had to alter a lot of votes to
get this effect (and in fact obtain a completely new election), I wouldn't
say it is a particularly outrageous failure of these axioms.
In general, the discussion about "which method is least vulnerable to
strategy" is quite arbitrary and hand-wavy for me in the situation where
all the methods are vulnerable and there is no single objective measure of
this vulnerability. And the arguments based on that don't justify
sacrificing the quality of the winner under sincere votes. For your example
with 46: A, 44: B>C, 10: C, I really can't convince myself that electing C
is justified. The argument that "B's supporters could have a preference of
B or B>A instead of B>C, and then B would have lost" is not convincing to
me if we only have the actual results of the election and don't know if
such an alternative scenario was even seriously considered by B's
supporters. Your argument with "Possible Approval Winner" is more
convincing, but I have two problems with it:
(1) A practical one: if you want to use AV as a justification, you
additionally need to explain AV to people, convince them that AV is a good
method (so that the possibility of being the AV winner is a good
justification) and at the same time, convince them that it is a bad method
(so that you do not advocate for it but for Condorcet).
(2) A theoretical one: using AV as a quality measure, requires us to assume
that people have objective "approval sets" in mind. I don't believe so, but
even if we take this for granted, then it is arbitrary to assume that they
are non-empty. It is perfectly possible that some of A's supporters have a
weak preference of A>B=C but in fact do not like anyone, and the most
approved candidate is B.
"I look forward to reading someone's argument that electing A in my other
example is justified."
My honest and totally subjective opinion about this example is that the
preferences there are quite weird and (if they are sincere) I have little
intuition for or against any of these candidates. It's clear to me that B
is a better candidate than A, but it's also at least equally clear that C
is better than B and A is better than C. And WV would elect B in this
example even if you change 17: B>C to 17: B=C, where I would strongly lean
towards either A or C.
Best,
Grzegorz
czw., 26 cze 2025 o 23:31 Chris Benham cbenhamau@yahoo.com.au napisał(a):
46: A
44: B>C
10: C
WV elect C here, while margins elect B. In fact, if the above preferences
are honest, then B is clearly the best candidate, since he is the closest
to be the Condorcet winner.
I don't see "closest to the Condorcet winner" as being necessarily
especially positive, let alone the compelling consideration. The actual
voted CW has a strong case to be elected and of course must be in a
Condorcet method. But "close to" doesn't mean anything.
Imagine you are an A supporter, or simply a sane sensible person
(preferably one who has never heard of Condorcet or Margins). Who do you
think should win this election?
46 A
44 B
10 C
Let me guess that you agree with me that the answer is A. Now let's
change that a little bit to this:
46 A
44 B>C
10 C
By what bizarre stretch of the imagination has extra (second place) votes
for C strengthened any candidate other than C ? The winner should either
still be A (the Hare and Benham winner) or change to C (the WV and Margins
Sorted Approval(implicit) and Smith//Approval(implicit) winner).
Electing A or (especially) C would be extremely unstable - if just one
voter changes his preference from A to B, the result would switch to B
under any Condorcet rule.
I find this to be a very weak and bizarre argument. Any close election
(Condorcet or not) can be "unstable" in this way.
Moreover, B has much broader support than C (assuming that A's supporters
are truly indifferent between both).
Only C is voted above bottom on more than half the ballots. There was a
criterion suggested called something like "Possible Approval Winner" that
said that if the voters all inserted an approval cutoff in their rankings
either only approving those candidates they vote below no others or all
except those they vote below no others or anywhere in between, then a
candidate who can't possibly be the most approved candidate can't win.
In this example the most approved candidate can only be A or C.
My favourite Condorcet method is Margins Sorted Approval (explicit):
Voters rank however many candidates they wish and also indicate an
approval threshold. Initially order the candidates according to their
approval scores. Check the pairwise result of the adjacent pair of
candidates with smallest difference in their approval scores.(If there is a
tie for this then the lowest-ordered pair among the tied pairs.) If the
lower-ordered of the two pairwise beats the higher-ordered candidate, then
those two candidates change places in the order. Repeat this procedure to
the end. The candidate at the top of the final order is the winner.
(The "implicit" version is the same except that ranking is interpreted as
approval.)
In this example, depending on whether or not the B>C voters approve C,
the initial order (based on approval scores) is either A>B>C or C>A>B.
In neither case is any pair of adjacent candidates out of order pairwise,
i.e. in the first case A pairwise beats B and B pairwise beats C and in
the second case C pairwise beats A and A pairwise beats B. So either way
the initial order is the final order and so the winner is either A or C.
"Benham" is the simplest and best of the Hare-Condorcet hybrids.
Voters strictly rank from the top however many candidates they wish.
Before any and each elimination we check for a pairwise-beats-all candidate
among the remaining candidates and elect the first one we find. Until then
we one-at-a-time eliminate the candidate that is the highest voted
remaining candidate on the smallest number of ballots.
(Allowing above-bottom equal ranking makes Push-over strategy easier. I
suggest interpreting ballots that have more than one candidate at the same
rank as having truncated just above that rank. I have the same opinion
about Hare.)
These methods I prefer to Winning Votes. Margins is beyond the pale. I
look forward to reading someone's argument that electing A in my other
example is justified.
46 A>C
17 B
17 B>C
20 B=C
Chris Benham
On 26/06/2025 9:12 pm, Grzegorz Pierczyński wrote:
Hi all,
Thanks for all your comments, axioms and explanations! From what I see,
the justification of WV is indeed rather pragmatic and strategy-oriented,
which is quite a problem for me. I would really prefer to avoid answering
the question: "Why did your rule elect a bad candidate in this election?"
by saying "Well, because you might have been dishonest in some specific
way, and then this candidate wouldn't be so bad". I also agree with Juho
that "in large public real life Condorcet elections it is very difficult to
implement and coordinate successful malicious strategies".
For example, the second example of Chris rather convinces me to support
margins and oppose WV, than the other way around. Let's see:
46: A
44: B>C
10: C
WV elect C here, while margins elect B. In fact, if the above preferences
are honest, then B is clearly the best candidate, since he is the closest
to be the Condorcet winner. Electing A or (especially) C would be extremely
unstable - if just one voter changes his preference from A to B, the result
would switch to B under any Condorcet rule. Moreover, B has much broader
support than C (assuming that A's supporters are truly indifferent between
both). I really can't find a logical justification of electing C here if
the voters are honest.
On the other hand, if we assume that voters were strategic and the honest
opinion of the middle voters is B or B>A, then it means that a massive
number of voters colluded to vote strategically, in a situation where (1)
the result of the race between A and B was unpredictable before the
election and B had real chances to win anyway, (2) a lot of voters had a
fragile preference of either B=A or B=C, and such a "dirty" operation of B
could easily change their minds to (respectively) A>B and C>B. I just don't
see this happening in practice. I can agree that such a theoretical
possibility is bad, because violating strategyproofness generally is bad,
but there's nothing particularly worrisome for me here.
Best,
Grzegorz
czw., 26 cze 2025 o 05:57 Chris Benham cbenhamau@yahoo.com.au
napisał(a):
There is also the Non-Drastic Defense criterion, which says that if more
than half the voters vote X above Y and X no lower than equal-top then
Y can't win.
46 A>C (maybe sincere is A or A>B)
17 B
17 B>C
20 C=B (maybe sincere is C>B)
B>A 54-46, A>C 63-37, C>B 46-34.
Here B is above A and no lower than equal-top on more than half the
ballots, but Margins elects A. Winning Votes elects B.
Also Margins can fail Later-no-Help especially egregiously and elect the
weakest candidate:
46 A
44 B>C (sincere might be B or B>A)
10 C
Margins elects B (failing the Plurality criterion). How does the B
voters ranking C remotely justify switching the win from A to B?? A
pairwise beats and positionally dominates B, and C is ranked above
bottom on the most number of ballots. I can't accept any method that
elects B here. (Or A in the previous example.)
I have long since decided that resolving Condorcet top cycles by
deciding (on some basis or another) that some pairwise defeats are
"weaker" than others is a dead end. I vastly prefer 3 other Condorcet
methods: Margins Sorted Approval(explicit), Margins Sorted Approval
(implicit), and "Benham".
They all resist Burial better than Margins or Winning Votes, and Margins
Sorted Approval is very elegant.
Chris Benham
On 26/06/2025 1:50 am, Kevin Venzke via Election-Methods wrote:
Hi Grzegorz,
- What exactly are the axioms that Condorcet rules with WV satisfy,
but with
margins do not? (I'm only aware of the Plurality criterion)
Very few have been articulated, but:
- I have sometimes read that WV are better to prevent strategic
behavior of
the voters (without much details),
I do use the minimal defense criterion, which represents the notion
that a full
majority of voters can always get their way if they want to, so it will
reduce
compromise strategy for the majority if you just give them their way
when you
know what it is.
To me, WV resolution is an approximation of an ideal. I made a webpage
that
attempts to show what options are available for electing from a
provided cycle,
with the aim of avoiding compromise incentive when you can:
https://votingmethods.net/check
This doesn't always favor WV, and sometimes there are no actual
solutions.
but do you have any idea how to justify WV
more "intuitively" or "philosophically", assuming sincere votes?
Margins are
very easy to justify. I came up with two possible justifications for
WV here
(described below), but I'm not sure how convincing they could be for
the
general audience.
Here I'm not sure. I guess by "sincere votes" you mean that absence of a
pairwise preference indicates an expression that two candidates are
equal. Or
maybe that truncation is not different from explicit equal ranking.
- Don't you think it is "ugly" that the WV measure applied e.g., to
Schulze
or RP/MAM requires us to artificially exclude "50% vs. 50%" ties
between
candidates from consideration (or equivalently, to mark them as the
weakest)
That's never occurred to me actually. All non-wins are excluded from
consideration.
--- and that a victory "50%+1 vs. 50%-1" is rapidly considered to be
quite
strong, stronger than e.g., a "45% vs. 1%" victory (with 54% voters
who rank
both candidates equally)? Under margins, ties or close ties are
naturally
considered the weakest. How would you refute this argument?
Ideally by some kind of rephrasing. I don't know if this is possible,
but it
would be nice if the matter could be presented without making it feel
like the
defeats themselves have an interest in being respected.
Alternatively, you want to find a explanation where losing votes are
just
meaningless, because for the practical purposes (the strategic
incentive ones),
they are. You don't obtain a valid complaint against the method by
losing a
close race, you can only get one by winning races and losing anyway
because you
didn't lie.
(In a 51:49 matchup, those on the losing side have no power to lie and
change
the outcome (we hope), while there is considerable possibility that
those on the
51 side could lie and win (i.e. if they had not), because they
comprise more
than half the voters. With 45:1, there are decent odds that those on
the 45%
side could win by lying; your method could determine this to be sure,
if you
wanted, before ruling for instance that 45:1 prevails over a win of
40:39. WV is
just making a mathematically easy "best guess.")
Regarding pt. 2, here are my ideas for a high-level intuitive
principle behind
WV:
(1) "It is much harder (infinitely harder?) to convince a voter to
change his
mind from B<A to A>B, than it is to change his mind from A=B to A>B".
Then, in
particular, it is more probable that a "45% vs. 1%" victory would
become a
"45% vs. 55%" defeat, than that a "51% vs. 49%" victory would become a
defeat.
That has some familiarity to me. If the winning side has a full
majority then we
"know" it is right. In fact if you entertain the concept of an overall
"median
voter" it suggests to us something about what that voter thinks.
Though I understand that you want to suppose that the equalities are in
fact
sincere.
In that case, if it's 45% A>B, 54% A=B, 1% B>A, my observation would be
that the
median position is that A and B are equal. The 54% aren't just
abstaining, are
they? I don't think that's what the assumption of sincerity implies.
Your second idea is kind of suggestive of this actually... You're just
focusing
more on voters' desire for how the matchup is handled.
(2) "If a voter votes for A=B, then he is not neutral, but he is
actively
voting against treating the resolution of the matchup between A and B
as
important". Then, in particular, in the case of a "45% vs. 1%"
victory, we in
fact have 45% of voters who consider it important to resolve the
matchup in a
particular direction, and 55% of voters who think otherwise. This is a
smaller
number than for a "51% vs. 49%" victory.
I view this possibility of voters having such a sentiment, and acting
on it in
this way, more as something useful that WV enables. I don't think we
can say
it's intuitively the case that voters are meaning to do this.
Kevin
votingmethods.net
Election-Methods mailing list - see https://electorama.com/em for list
info
Hi Grzegorz,
Thanks for all your comments, axioms and explanations! From what I see, the
justification of WV is indeed rather pragmatic and strategy-oriented, which is
quite a problem for me. I would really prefer to avoid answering the question:
"Why did your rule elect a bad candidate in this election?" by saying "Well,
because you might have been dishonest in some specific way, and then this
candidate wouldn't be so bad". I also agree with Juho that "in large public
real life Condorcet elections it is very difficult to implement and coordinate
successful malicious strategies".
I would point out that in my discussion I never said anything about malicious
strategies. My /check webpage doesn't either. The strategies I talk about are
favorite betrayal, which are not malicious strategies, but strategies where
voters are trying to compensate for a method not working well enough.
I think this is a mistake in how WV is often defended. It's true that if you
take care to minimize compromise incentive (which is, I think, what WV wants to
do; and actually, I dare say, it's what Condorcet wants to do) then this can be
useful in stopping other voters from carrying out a scheme. But this isn't the
goal of minimizing compromise incentive.
For example, the second example of Chris rather convinces me to support margins
and oppose WV, than the other way around. Let's see:
46: A
44: B>C
10: C
WV elect C here, while margins elect B. In fact, if the above preferences are
honest, then B is clearly the best candidate, since he is the closest to be the
Condorcet winner. Electing A or (especially) C would be extremely unstable - if
just one voter changes his preference from A to B, the result would switch to B
under any Condorcet rule. Moreover, B has much broader support than C (assuming
that A's supporters are truly indifferent between both). I really can't find a
logical justification of electing C here if the voters are honest.
Alright, but I think it would be very strange if these were honest votes in a
public election. I look at that, as a real election, and suspect a similarity
between candidates B and C, and that the A voters dislike both and don't want to
risk helping either against the other.
(You could say I'm assuming the incentives are as under WV, but I think we've
seen that even IRV voters truncate like this.)
On the other hand, if we assume that voters were strategic and the honest
opinion of the middle voters is B or B>A, then it means that a massive number
of voters colluded to vote strategically, in a situation where (1) the result
of the race between A and B was unpredictable before the election and B had
real chances to win anyway, (2) a lot of voters had a fragile preference of
either B=A or B=C, and such a "dirty" operation of B could easily change their
minds to (respectively) A>B and C>B. I just don't see this happening in
practice. I can agree that such a theoretical possibility is bad, because
violating strategyproofness generally is bad, but there's nothing particularly
worrisome for me here.
For me this is a strange example. If you plug it into /check, there is no
compromise incentive issue with electing B. Rather, you're defending a failure
of the Plurality criterion. Typically such scenarios aren't used to speculate
about malicious strategy potential. Tentatively I'd agree that it's not
"worrisome" in that way.
Kevin
votingmethods.net