The rationale under the "winning votes" defeat strength measure
Grzegorz,
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.
No, not a "completely new election". Say the first one is the result of
a completely accurate poll. Say all the voters really want their
favourites to win and their preferences among their non-favourites are
very weak or non-existent.
46 A
44 B
10 C
Come the actual election the A supporters think "We are the largest
faction and we know this method fails Later-no-Harm, so we shall (quite
sincerely) truncate." The B supporters think "If we (sincerely)
truncate then we will almost certainly lose to A. We know this method
fails Later-no-Help, so why don't we rank C in second place and see what
happens? This can't do any harm because C is on 10% and so presumably
can't win, and/or if our favourite B can't win then we don't care who
wins." The C voters think "We don't like or care about A or B. We are
just here to fly the flag for our candidate with a view to maybe being
competitive in a future election."
So in the actual election we get:
46 A
44 B>C
10 C
And Margins elects B. Yes all Condorcet methods fail Later-no-Help, but
this is an especially egregious and simple example. And it is combined
with a failure of the Plurality criterion, which says that if A has more
first-place votes than B has any (above-bottom) votes then B can't win.
I like something similar, that says if A both positionally dominates B
and pairwise beats B, then B can't win. By "positionally dominate" I
mean that A has more first place votes, more first and second place
votes, and so on down to more above-bottom votes.)
So forget about C for the time being and just focus on the A>B pairwise
comparison. To any person who doesn't fetishise the Margins algorithm
and has some common sense, there is no case for A losing to B. When the
A supporters ask you "How did our candidate lose to B?? We understand
this is some sort of preferential system, but B got no second-place
votes and A got more first-place votes" you tell them what? Do you
really think that they will and should be satisfied with some
mumbo-jumbo about B being "closer to being the CW"?
You and Juho like to talk about "stability". Do you really think that
(if the stakes are high) that this (social stability) is enhanced by
you openly shafting the largest faction??
Hopefully I have now got it through your skull that B is an
unacceptable winner due to A. So what about the C>A comparison? The
WV philosophy is that if there is no voted CW and enough truncation then
it is possible that there is a sincere CW due to some sincere
preferences that the truncation is concealing and so it is important
that we elect one of the candidates who could be that sincere CW.
C has a pairwise win over A that can't be undone by filling in some
truncated ballots in a way that favours A, so A can't be this
(hypothetical, imaginary) "sincere CW". But C's pairwise loss to B
could go away if the A truncating ballots were filled in (changed) to A>C.
So WV elects C.
But I am not on board with this philosophy. If voters choose not to
express some of their pairwise preferences I don't see how doing
anything other than simply assuming they don't exist is justified.
It could be that the only insincerity is the C faction truncating
against B, so B is the sincere CW and electing C is letting that faction
get away with defecting from the presumed BC coalition.
That is one of the main reasons I like Margins Sorted Approval
(explicit). If the B<C voters have beating A no-matter-what as a high
priority then they can approve C. If on the other hand they were
expecting the C supporters to return the favour and vote C>B and they
want to ensure that they can't steal the election from B by defecting
then they can approve B only.
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.
Possibly, but why do you assume that this approach is correct?
Chris Benham
On 27/06/2025 8:10 pm, Grzegorz Pierczyński wrote:
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."
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 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 http://votingmethods.net
Election-Methods mailing list - see
https://electorama.com/em for list info
Chris,
Once again -- your argumentation is based on the assumption that
preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences
are 46: A, 44: B, 10: C. I see no reason for a voting rule to presume that,
having only the actual results in hand. But even if we accept this
assumption, it only demonstrates that Margins can violate IIA/Later-no-help
(bad, but unavoidable for Condorcet) if you alter preferences in 44 votes
out of 100 (quite a lot). In the same way you could e.g., presume that the
real preferences are 46: A, 44: B>C, 2: C>B, 8: C and then WV would violate
Later-no-harm with only altering 2 votes out of 100, while Margins would be
resistant to that. In fact, the "stability" of Margins provides us (as a
side effect) that, since it is harder than under WV to alter the result by
changing preferences of a tiny fraction of the voters, it is also harder to
successfully strategize by a tiny fraction of the voters.
In general, I haven't seen a convincing argument that C is a good winner
under honest votes in this election and to me it would be more egregious to
say to B's supporters "the rule elected C instead of B, because it presumed
that your preference C>A was dishonest" than to say to A's supporters: "No
rule could respect all pairwise defeats between A, B and C, and the one
between A and B was the least decisive. If you only cared about having A
elected, then sorry, but 54 voters preferred C. And according to your
preferences B is as good choice as C, so if you preferred C to be elected,
you should have voted A>C, not A".
I don't believe our discussion is decidable so maybe we have reached the
point where we should just "agree to disagree" on that matter.
Grzegorz
niedz., 29 cze 2025, 02:46 użytkownik Chris Benham cbenhamau@yahoo.com.au
napisał:
Grzegorz,
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.
No, not a "completely new election". Say the first one is the result of a
completely accurate poll. Say all the voters really want their favourites
to win and their preferences among their non-favourites are very weak or
non-existent.
46 A
44 B
10 C
Come the actual election the A supporters think "We are the largest
faction and we know this method fails Later-no-Harm, so we shall (quite
sincerely) truncate." The B supporters think "If we (sincerely) truncate
then we will almost certainly lose to A. We know this method fails
Later-no-Help, so why don't we rank C in second place and see what
happens? This can't do any harm because C is on 10% and so presumably
can't win, and/or if our favourite B can't win then we don't care who
wins." The C voters think "We don't like or care about A or B. We are just
here to fly the flag for our candidate with a view to maybe being
competitive in a future election."
So in the actual election we get:
46 A
44 B>C
10 C
And Margins elects B. Yes all Condorcet methods fail Later-no-Help, but
this is an especially egregious and simple example. And it is combined with
a failure of the Plurality criterion, which says that if A has more
first-place votes than B has any (above-bottom) votes then B can't win. I
like something similar, that says if A both positionally dominates B and
pairwise beats B, then B can't win. By "positionally dominate" I mean that
A has more first place votes, more first and second place votes, and so on
down to more above-bottom votes.)
So forget about C for the time being and just focus on the A>B pairwise
comparison. To any person who doesn't fetishise the Margins algorithm and
has some common sense, there is no case for A losing to B. When the A
supporters ask you "How did our candidate lose to B?? We understand this is
some sort of preferential system, but B got no second-place votes and A got
more first-place votes" you tell them what? Do you really think that they
will and should be satisfied with some mumbo-jumbo about B being "closer to
being the CW"?
You and Juho like to talk about "stability". Do you really think that (if
the stakes are high) that this (social stability) is enhanced by you
openly shafting the largest faction??
Hopefully I have now got it through your skull that B is an unacceptable
winner due to A. So what about the C>A comparison? The WV philosophy is
that if there is no voted CW and enough truncation then it is possible that
there is a sincere CW due to some sincere preferences that the truncation
is concealing and so it is important that we elect one of the candidates
who could be that sincere CW.
C has a pairwise win over A that can't be undone by filling in some
truncated ballots in a way that favours A, so A can't be this
(hypothetical, imaginary) "sincere CW". But C's pairwise loss to B could
go away if the A truncating ballots were filled in (changed) to A>C.
So WV elects C.
But I am not on board with this philosophy. If voters choose not to
express some of their pairwise preferences I don't see how doing anything
other than simply assuming they don't exist is justified.
It could be that the only insincerity is the C faction truncating against
B, so B is the sincere CW and electing C is letting that faction get away
with defecting from the presumed BC coalition.
That is one of the main reasons I like Margins Sorted Approval (explicit).
If the B<C voters have beating A no-matter-what as a high priority then
they can approve C. If on the other hand they were expecting the C
supporters to return the favour and vote C>B and they want to ensure that
they can't steal the election from B by defecting then they can approve B
only.
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.
Possibly, but why do you assume that this approach is correct?
Chris Benham
On 27/06/2025 8:10 pm, Grzegorz Pierczyński wrote:
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."
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 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
On 06/29/2025 1:42 PM EDT Grzegorz Pierczyński via Election-Methods election-methods@lists.electorama.com wrote:
...
I see no reason for a voting rule to presume that, having only the actual results in hand.
What other data can we use?
This is soooo blatantly obvious.
I just cannot understand designing and constructing a voting system that is not a fully deterministic function of the actual valid ballots cast. This is why I could not get past Square 1 with some of Chris's arguments. Yes, some people vote tactically. How will we ever know? Shall we put a check box on the ballot that says "this ballot is not marked sincerely" so then the method can change the rule for how that voter's vote shall be counted?
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Once again -- your argumentation is based on the assumption that
preferences 46: A, 44: B>C, 10: C are not honest and the "real"
preferences are 46: A, 44: B, 10: C.
Not entirely. I am arguing that electing B is a complete nonsense
result regardless of whether the votes are sincere or not due to the
egregious failure of the Plurality criterion. I am not arguing that WV
is a great method or even that is in every way superior to Margins.
The A supporter's complaint against the Margins result is not that C
didn't win, it is that their candidate was defeated by B. Suppose this
is the first post FPP election, the A supporters were quite happy with
FPP and are not interested in either the preferential voting algorithm
at least partly because they dislike both the other candidates
equally. Their complaint is that their candidate clearly has more
support on the ballots than B, and whatever convoluted
algorithm/argument that says that B should win must be BS.
"No rule could respect all pairwise defeats between A, B and C, and
the one between A and B was the least decisive. If you only cared
about having A elected, then sorry, but 54 voters preferred C. And
according to your preferences B is as good choice as C, so if you
preferred C to be elected, you should have voted A>C, not A".
And they are right.
..to me it would be more egregious to say to B's supporters "the rule
elected C instead of B, because it presumed that your preference C>A
was dishonest"
I don't see why, but my answer to the B supporters' complaint would be
"You cannot imagine that your candidate should be elected because A has
more first-place votes than your candidate has any sort of votes. C has
more (some sort of ) votes than B. No-one told you that this method
meets Later-no-Harm so why did you rank C if you are not content for C
to win?"
That to me very easily trumps "Oh but according to the Margins algorithm
B was the closest to being the Condorcet winner."
Answering the A supporters' possible complaint against C winning is not
too difficult: "C pairwise beats A and is ranked above bottom on more
ballots than A. Electing A could cause the B>C voters to regret not
voting B=C or C>B or C".
I don't believe our discussion is decidable so maybe we have reached
the point where we should just "agree to disagree" on that matter.
If this discussion was private I might have come to the same conclusion
sooner. You have ignored several of my direct questions.
Chris
On 30/06/2025 3:12 am, Grzegorz Pierczyński via Election-Methods wrote:
Chris,
Once again -- your argumentation is based on the assumption that
preferences 46: A, 44: B>C, 10: C are not honest and the "real"
preferences are 46: A, 44: B, 10: C. I see no reason for a voting rule
to presume that, having only the actual results in hand. But even if
we accept this assumption, it only demonstrates that Margins can
violate IIA/Later-no-help (bad, but unavoidable for Condorcet) if you
alter preferences in 44 votes out of 100 (quite a lot). In the same
way you could e.g., presume that the real preferences are 46: A, 44:
B>C, 2: C>B, 8: C and then WV would violate Later-no-harm with
only altering 2 votes out of 100, while Margins would be resistant to
that. In fact, the "stability" of Margins provides us (as a side
effect) that, since it is harder than under WV to alter the result by
changing preferences of a tiny fraction of the voters, it is also
harder to successfully strategize by a tiny fraction of the voters.
In general, I haven't seen a convincing argument that C is a good
winner under honest votes in this election and to me it would be more
egregious to say to B's supporters "the rule elected C instead of B,
because it presumed that your preference C>A was dishonest" than to
say to A's supporters: "No rule could respect all pairwise defeats
between A, B and C, and the one between A and B was the least
decisive. If you only cared about having A elected, then sorry, but 54
voters preferred C. And according to your preferences B is as good
choice as C, so if you preferred C to be elected, you should have
voted A>C, not A".
I don't believe our discussion is decidable so maybe we have reached
the point where we should just "agree to disagree" on that matter.
Grzegorz
niedz., 29 cze 2025, 02:46 użytkownik Chris Benham
cbenhamau@yahoo.com.au napisał:
Grzegorz,
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.
No, not a "completely new election". Say the first one is the
result of a completely accurate poll. Say all the voters really
want their favourites to win and their preferences among their
non-favourites are very weak or non-existent.
46 A
44 B
10 C
Come the actual election the A supporters think "We are the
largest faction and we know this method fails Later-no-Harm, so we
shall (quite sincerely) truncate." The B supporters think "If we
(sincerely) truncate then we will almost certainly lose to A. We
know this method fails Later-no-Help, so why don't we rank C in
second place and see what happens? This can't do any harm because
C is on 10% and so presumably can't win, and/or if our favourite B
can't win then we don't care who wins." The C voters think "We
don't like or care about A or B. We are just here to fly the flag
for our candidate with a view to maybe being competitive in a
future election."
So in the actual election we get:
46 A
44 B>C
10 C
And Margins elects B. Yes all Condorcet methods fail
Later-no-Help, but this is an especially egregious and simple
example. And it is combined with a failure of the Plurality
criterion, which says that if A has more first-place votes than B
has any (above-bottom) votes then B can't win. I like something
similar, that says if A both positionally dominates B and pairwise
beats B, then B can't win. By "positionally dominate" I mean that
A has more first place votes, more first and second place votes,
and so on down to more above-bottom votes.)
So forget about C for the time being and just focus on the A>B
pairwise comparison. To any person who doesn't fetishise the
Margins algorithm and has some common sense, there is no case for
A losing to B. When the A supporters ask you "How did our
candidate lose to B?? We understand this is some sort of
preferential system, but B got no second-place votes and A got
more first-place votes" you tell them what? Do you really think
that they will and should be satisfied with some mumbo-jumbo about
B being "closer to being the CW"?
You and Juho like to talk about "stability". Do you really think
that (if the stakes are high) that this (social stability) is
enhanced by you openly shafting the largest faction??
Hopefully I have now got it through your skull that B is an
unacceptable winner due to A. So what about the C>A
comparison? The WV philosophy is that if there is no voted CW and
enough truncation then it is possible that there is a sincere CW
due to some sincere preferences that the truncation is concealing
and so it is important that we elect one of the candidates who
could be that sincere CW.
C has a pairwise win over A that can't be undone by filling in
some truncated ballots in a way that favours A, so A can't be
this (hypothetical, imaginary) "sincere CW". But C's pairwise
loss to B could go away if the A truncating ballots were filled in
(changed) to A>C.
So WV elects C.
But I am not on board with this philosophy. If voters choose not
to express some of their pairwise preferences I don't see how
doing anything other than simply assuming they don't exist is
justified.
It could be that the only insincerity is the C faction truncating
against B, so B is the sincere CW and electing C is letting that
faction get away with defecting from the presumed BC coalition.
That is one of the main reasons I like Margins Sorted Approval
(explicit). If the B<C voters have beating A no-matter-what as a
high priority then they can approve C. If on the other hand they
were expecting the C supporters to return the favour and vote C>B
and they want to ensure that they can't steal the election from B
by defecting then they can approve B only.
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.
Possibly, but why do you assume that this approach is correct?
Chris Benham
On 27/06/2025 8:10 pm, Grzegorz Pierczyński wrote:
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."
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 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:
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.
https://electorama.com/em for list info
Election-Methods mailing list - seehttps://electorama.com/em for list info
Hi,
I think it is quite natural that the circular Condorcet examples can be seen from multiple viewpoints (even too many to cover them all), based on what one is studying, what one is seeking to prove, what the details of the given example happen to be, and where one's random thoughts might lead him to. E.g. are the described votes sincere or strategic, and what the original sincere preferences could be, what alternative strategic votes there could be, or who would be the best winner (in the absence of a Condorcet winner). Discussions on the EM list have been active for many years, and still are. It is far from easy to pack the final conclusions from the numerous, typically cyclic voting scenarios in few sentences that everyone would agree.
One problem is that we often tend to focus and limit ourselves to "laboratory examples" where all the preferences of the voters are 100% known, they are 100% stable, and we can 100% decide what kind of (sincere of strategic) votes the voters will cast, usually as few uniform blocks of voters. With that we can typically prove that something like that would be theoretically possible also in real life elections. But in order to draw more stable conclusions on how different methods tend to behave in real life elections, we would have to include in the picture also changes in time and inaccuracy of the (multiple) polls, later changes in the opinions of the voters, possible multiple rational and irrational strategic plans, strategies of individual voters, strategies recommended by experts (from the party office), ability of those experts to influence on how people vote, willingness and ability of the voters to follow the proposed strategies, reactions of voters to the plans to "fool the system", high number of different preferences among the voters (not just three of four) etc. That is a softer and more difficult target to reach.
I think we are still missing a "generic short handbook for voters on how to vote in real life elections". How close do we get by saying "just vote sincerely", or by saying "just let the party office tell you how to vote in these elections"? (maybe a separate handbook needed for those party strategists?)
One question that was also present in this discussion is how much emphasis we should put on defending against some strategic voting threats vs how much we should concentrate on providing best results with sincere votes. We need to convince the voters (and the politicians) that the proposed method behaves well, any make sure that the method is understandable, and its philosophy makes sense to them. Different audiences may have different needs, voting traditions, fears, and old habits that they need to learn away from.
Most people on this list (including me) agree that Condorcet methods might have something to offer to the world. Condorcet methods are quite good in general, of course depending on if the compromise seeking philosophy of Condorcet methods is what the society needs and wants (instead of e.g. allowing the first preference plurality winner always win).
Juho
On 30. Jun 2025, at 7.59, Chris Benham cbenhamau@yahoo.com.au wrote:
Once again -- your argumentation is based on the assumption that preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences are 46: A, 44: B, 10: C.
Not entirely. I am arguing that electing B is a complete nonsense result regardless of whether the votes are sincere or not due to the egregious failure of the Plurality criterion. I am not arguing that WV is a great method or even that is in every way superior to Margins.
The A supporter's complaint against the Margins result is not that C didn't win, it is that their candidate was defeated by B. Suppose this is the first post FPP election, the A supporters were quite happy with FPP and are not interested in either the preferential voting algorithm at least partly because they dislike both the other candidates equally. Their complaint is that their candidate clearly has more support on the ballots than B, and whatever convoluted algorithm/argument that says that B should win must be BS.
"No rule could respect all pairwise defeats between A, B and C, and the one between A and B was the least decisive. If you only cared about having A elected, then sorry, but 54 voters preferred C. And according to your preferences B is as good choice as C, so if you preferred C to be elected, you should have voted A>C, not A".
And they are right.
..to me it would be more egregious to say to B's supporters "the rule elected C instead of B, because it presumed that your preference C>A was dishonest"
I don't see why, but my answer to the B supporters' complaint would be "You cannot imagine that your candidate should be elected because A has more first-place votes than your candidate has any sort of votes. C has more (some sort of ) votes than B. No-one told you that this method meets Later-no-Harm so why did you rank C if you are not content for C to win?"
That to me very easily trumps "Oh but according to the Margins algorithm B was the closest to being the Condorcet winner."
Answering the A supporters' possible complaint against C winning is not too difficult: "C pairwise beats A and is ranked above bottom on more ballots than A. Electing A could cause the B>C voters to regret not voting B=C or C>B or C".
I don't believe our discussion is decidable so maybe we have reached the point where we should just "agree to disagree" on that matter.
If this discussion was private I might have come to the same conclusion sooner. You have ignored several of my direct questions.
Chris
On 30/06/2025 3:12 am, Grzegorz Pierczyński via Election-Methods wrote:
Chris,
Once again -- your argumentation is based on the assumption that preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences are 46: A, 44: B, 10: C. I see no reason for a voting rule to presume that, having only the actual results in hand. But even if we accept this assumption, it only demonstrates that Margins can violate IIA/Later-no-help (bad, but unavoidable for Condorcet) if you alter preferences in 44 votes out of 100 (quite a lot). In the same way you could e.g., presume that the real preferences are 46: A, 44: B>C, 2: C>B, 8: C and then WV would violate Later-no-harm with only altering 2 votes out of 100, while Margins would be resistant to that. In fact, the "stability" of Margins provides us (as a side effect) that, since it is harder than under WV to alter the result by changing preferences of a tiny fraction of the voters, it is also harder to successfully strategize by a tiny fraction of the voters.
In general, I haven't seen a convincing argument that C is a good winner under honest votes in this election and to me it would be more egregious to say to B's supporters "the rule elected C instead of B, because it presumed that your preference C>A was dishonest" than to say to A's supporters: "No rule could respect all pairwise defeats between A, B and C, and the one between A and B was the least decisive. If you only cared about having A elected, then sorry, but 54 voters preferred C. And according to your preferences B is as good choice as C, so if you preferred C to be elected, you should have voted A>C, not A".
I don't believe our discussion is decidable so maybe we have reached the point where we should just "agree to disagree" on that matter.
Grzegorz
niedz., 29 cze 2025, 02:46 użytkownik Chris Benham <cbenhamau@yahoo.com.au mailto:cbenhamau@yahoo.com.au> napisał:
Grzegorz,
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.
No, not a "completely new election". Say the first one is the result of a completely accurate poll. Say all the voters really want their favourites to win and their preferences among their non-favourites are very weak or non-existent.
46 A
44 B
10 C
Come the actual election the A supporters think "We are the largest faction and we know this method fails Later-no-Harm, so we shall (quite sincerely) truncate." The B supporters think "If we (sincerely) truncate then we will almost certainly lose to A. We know this method fails Later-no-Help, so why don't we rank C in second place and see what happens? This can't do any harm because C is on 10% and so presumably can't win, and/or if our favourite B can't win then we don't care who wins." The C voters think "We don't like or care about A or B. We are just here to fly the flag for our candidate with a view to maybe being competitive in a future election."
So in the actual election we get:
46 A
44 B>C
10 C
And Margins elects B. Yes all Condorcet methods fail Later-no-Help, but this is an especially egregious and simple example. And it is combined with a failure of the Plurality criterion, which says that if A has more first-place votes than B has any (above-bottom) votes then B can't win. I like something similar, that says if A both positionally dominates B and pairwise beats B, then B can't win. By "positionally dominate" I mean that A has more first place votes, more first and second place votes, and so on down to more above-bottom votes.)
So forget about C for the time being and just focus on the A>B pairwise comparison. To any person who doesn't fetishise the Margins algorithm and has some common sense, there is no case for A losing to B. When the A supporters ask you "How did our candidate lose to B?? We understand this is some sort of preferential system, but B got no second-place votes and A got more first-place votes" you tell them what? Do you really think that they will and should be satisfied with some mumbo-jumbo about B being "closer to being the CW"?
You and Juho like to talk about "stability". Do you really think that (if the stakes are high) that this (social stability) is enhanced by you openly shafting the largest faction??
Hopefully I have now got it through your skull that B is an unacceptable winner due to A. So what about the C>A comparison? The WV philosophy is that if there is no voted CW and enough truncation then it is possible that there is a sincere CW due to some sincere preferences that the truncation is concealing and so it is important that we elect one of the candidates who could be that sincere CW.
C has a pairwise win over A that can't be undone by filling in some truncated ballots in a way that favours A, so A can't be this (hypothetical, imaginary) "sincere CW". But C's pairwise loss to B could go away if the A truncating ballots were filled in (changed) to A>C.
So WV elects C.
But I am not on board with this philosophy. If voters choose not to express some of their pairwise preferences I don't see how doing anything other than simply assuming they don't exist is justified.
It could be that the only insincerity is the C faction truncating against B, so B is the sincere CW and electing C is letting that faction get away with defecting from the presumed BC coalition.
That is one of the main reasons I like Margins Sorted Approval (explicit). If the B<C voters have beating A no-matter-what as a high priority then they can approve C. If on the other hand they were expecting the C supporters to return the favour and vote C>B and they want to ensure that they can't steal the election from B by defecting then they can approve B only.
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.
Possibly, but why do you assume that this approach is correct?
Chris Benham
On 27/06/2025 8:10 pm, Grzegorz Pierczyński wrote:
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."
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 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 mailto: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 mailto: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
Election-Methods mailing list - see https://electorama.com/em for list info
*Once again -- your argumentation is based on the assumption that
preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences
are 46: A, 44: B, 10: C. I see no reason for a voting rule to presume that,
having only the actual results in hand. *
If we’re assuming complete honesty from the voters, score voting becomes
optimal almost by definition (or by Harsanyi’s utilitarian theorem). The
advantage of median and Condorcet rules is supposed to be better
performance if only some voters strategically exaggerate.
The major issue for margins is that, with strategic voters, the election
results become effectively random just like for Borda, and even a
universally-ranked-last candidate can win. The mailing list calls this DH3
and talks about “burial resistance criteria”, but I find this focus on
criteria instead of specific models of election outcomes kind of silly, so
I’ll say it’s better explained in Burt Monroe’s turkey-raising paper, where
he games out Myerson-Satterthwaite-style equilibria.
On Mon, Jun 30, 2025 at 1:36 AM Juho Laatu via Election-Methods <
election-methods@lists.electorama.com> wrote:
Hi,
I think it is quite natural that the circular Condorcet examples can be
seen from multiple viewpoints (even too many to cover them all), based on
what one is studying, what one is seeking to prove, what the details of the
given example happen to be, and where one's random thoughts might lead him
to. E.g. are the described votes sincere or strategic, and what the
original sincere preferences could be, what alternative strategic votes
there could be, or who would be the best winner (in the absence of a
Condorcet winner). Discussions on the EM list have been active for many
years, and still are. It is far from easy to pack the final conclusions
from the numerous, typically cyclic voting scenarios in few sentences that
everyone would agree.
One problem is that we often tend to focus and limit ourselves to
"laboratory examples" where all the preferences of the voters are 100%
known, they are 100% stable, and we can 100% decide what kind of (sincere
of strategic) votes the voters will cast, usually as few uniform blocks of
voters. With that we can typically prove that something like that would be
theoretically possible also in real life elections. But in order to draw
more stable conclusions on how different methods tend to behave in real
life elections, we would have to include in the picture also changes in
time and inaccuracy of the (multiple) polls, later changes in the opinions
of the voters, possible multiple rational and irrational strategic plans,
strategies of individual voters, strategies recommended by experts (from
the party office), ability of those experts to influence on how people
vote, willingness and ability of the voters to follow the proposed
strategies, reactions of voters to the plans to "fool the system", high
number of different preferences among the voters (not just three of four)
etc. That is a softer and more difficult target to reach.
I think we are still missing a "generic short handbook for voters on how
to vote in real life elections". How close do we get by saying "just vote
sincerely", or by saying "just let the party office tell you how to vote in
these elections"? (maybe a separate handbook needed for those party
strategists?)
One question that was also present in this discussion is how much emphasis
we should put on defending against some strategic voting threats vs how
much we should concentrate on providing best results with sincere votes. We
need to convince the voters (and the politicians) that the proposed method
behaves well, any make sure that the method is understandable, and its
philosophy makes sense to them. Different audiences may have different
needs, voting traditions, fears, and old habits that they need to learn
away from.
Most people on this list (including me) agree that Condorcet methods might
have something to offer to the world. Condorcet methods are quite good in
general, of course depending on if the compromise seeking philosophy of
Condorcet methods is what the society needs and wants (instead of e.g.
allowing the first preference plurality winner always win).
Juho
On 30. Jun 2025, at 7.59, Chris Benham cbenhamau@yahoo.com.au wrote:
Once again -- your argumentation is based on the assumption that
preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences
are 46: A, 44: B, 10: C.
Not entirely. I am arguing that electing B is a complete nonsense result
regardless of whether the votes are sincere or not due to the egregious
failure of the Plurality criterion. I am not arguing that WV is a great
method or even that is in every way superior to Margins.
The A supporter's complaint against the Margins result is not that C
didn't win, it is that their candidate was defeated by B. Suppose this is
the first post FPP election, the A supporters were quite happy with FPP and
are not interested in either the preferential voting algorithm at least
partly because they dislike both the other candidates equally. Their
complaint is that their candidate clearly has more support on the ballots
than B, and whatever convoluted algorithm/argument that says that B should
win must be BS.
"No rule could respect all pairwise defeats between A, B and C, and the
one between A and B was the least decisive. If you only cared about having
A elected, then sorry, but 54 voters preferred C. And according to your
preferences B is as good choice as C, so if you preferred C to be elected,
you should have voted A>C, not A".
And they are right.
..to me it would be more egregious to say to B's supporters "the rule
elected C instead of B, because it presumed that your preference C>A was
dishonest"
I don't see why, but my answer to the B supporters' complaint would be
"You cannot imagine that your candidate should be elected because A has
more first-place votes than your candidate has any sort of votes. C has
more (some sort of ) votes than B. No-one told you that this method meets
Later-no-Harm so why did you rank C if you are not content for C to win?"
That to me very easily trumps "Oh but according to the Margins algorithm B
was the closest to being the Condorcet winner."
Answering the A supporters' possible complaint against C winning is not
too difficult: "C pairwise beats A and is ranked above bottom on more
ballots than A. Electing A could cause the B>C voters to regret not voting
B=C or C>B or C".
I don't believe our discussion is decidable so maybe we have reached the
point where we should just "agree to disagree" on that matter.
If this discussion was private I might have come to the same conclusion
sooner. You have ignored several of my direct questions.
Chris
On 30/06/2025 3:12 am, Grzegorz Pierczyński via Election-Methods wrote:
Chris,
Once again -- your argumentation is based on the assumption that
preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences
are 46: A, 44: B, 10: C. I see no reason for a voting rule to presume that,
having only the actual results in hand. But even if we accept this
assumption, it only demonstrates that Margins can violate IIA/Later-no-help
(bad, but unavoidable for Condorcet) if you alter preferences in 44 votes
out of 100 (quite a lot). In the same way you could e.g., presume that the
real preferences are 46: A, 44: B>C, 2: C>B, 8: C and then WV would violate
Later-no-harm with only altering 2 votes out of 100, while Margins would be
resistant to that. In fact, the "stability" of Margins provides us (as a
side effect) that, since it is harder than under WV to alter the result by
changing preferences of a tiny fraction of the voters, it is also harder to
successfully strategize by a tiny fraction of the voters.
In general, I haven't seen a convincing argument that C is a good winner
under honest votes in this election and to me it would be more egregious to
say to B's supporters "the rule elected C instead of B, because it presumed
that your preference C>A was dishonest" than to say to A's supporters: "No
rule could respect all pairwise defeats between A, B and C, and the one
between A and B was the least decisive. If you only cared about having A
elected, then sorry, but 54 voters preferred C. And according to your
preferences B is as good choice as C, so if you preferred C to be elected,
you should have voted A>C, not A".
I don't believe our discussion is decidable so maybe we have reached the
point where we should just "agree to disagree" on that matter.
Grzegorz
niedz., 29 cze 2025, 02:46 użytkownik Chris Benham cbenhamau@yahoo.com.au
napisał:
Grzegorz,
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.
No, not a "completely new election". Say the first one is the result of
a completely accurate poll. Say all the voters really want their favourites
to win and their preferences among their non-favourites are very weak or
non-existent.
46 A
44 B
10 C
Come the actual election the A supporters think "We are the largest
faction and we know this method fails Later-no-Harm, so we shall (quite
sincerely) truncate." The B supporters think "If we (sincerely) truncate
then we will almost certainly lose to A. We know this method fails
Later-no-Help, so why don't we rank C in second place and see what
happens? This can't do any harm because C is on 10% and so presumably
can't win, and/or if our favourite B can't win then we don't care who
wins." The C voters think "We don't like or care about A or B. We are just
here to fly the flag for our candidate with a view to maybe being
competitive in a future election."
So in the actual election we get:
46 A
44 B>C
10 C
And Margins elects B. Yes all Condorcet methods fail Later-no-Help, but
this is an especially egregious and simple example. And it is combined with
a failure of the Plurality criterion, which says that if A has more
first-place votes than B has any (above-bottom) votes then B can't win. I
like something similar, that says if A both positionally dominates B and
pairwise beats B, then B can't win. By "positionally dominate" I mean that
A has more first place votes, more first and second place votes, and so on
down to more above-bottom votes.)
So forget about C for the time being and just focus on the A>B pairwise
comparison. To any person who doesn't fetishise the Margins algorithm and
has some common sense, there is no case for A losing to B. When the A
supporters ask you "How did our candidate lose to B?? We understand this is
some sort of preferential system, but B got no second-place votes and A got
more first-place votes" you tell them what? Do you really think that they
will and should be satisfied with some mumbo-jumbo about B being "closer to
being the CW"?
You and Juho like to talk about "stability". Do you really think that
(if the stakes are high) that this (social stability) is enhanced by you
openly shafting the largest faction??
Hopefully I have now got it through your skull that B is an unacceptable
winner due to A. So what about the C>A comparison? The WV philosophy is
that if there is no voted CW and enough truncation then it is possible that
there is a sincere CW due to some sincere preferences that the truncation
is concealing and so it is important that we elect one of the candidates
who could be that sincere CW.
C has a pairwise win over A that can't be undone by filling in some
truncated ballots in a way that favours A, so A can't be this
(hypothetical, imaginary) "sincere CW". But C's pairwise loss to B could
go away if the A truncating ballots were filled in (changed) to A>C.
So WV elects C.
But I am not on board with this philosophy. If voters choose not to
express some of their pairwise preferences I don't see how doing anything
other than simply assuming they don't exist is justified.
It could be that the only insincerity is the C faction truncating against
B, so B is the sincere CW and electing C is letting that faction get away
with defecting from the presumed BC coalition.
That is one of the main reasons I like Margins Sorted Approval
(explicit). If the B<C voters have beating A no-matter-what as a high
priority then they can approve C. If on the other hand they were expecting
the C supporters to return the favour and vote C>B and they want to ensure
that they can't steal the election from B by defecting then they can
approve B only.
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.
Possibly, but why do you assume that this approach is correct?
Chris Benham
On 27/06/2025 8:10 pm, Grzegorz Pierczyński wrote:
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."
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 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
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On 07/01/2025 3:24 PM EDT Closed Limelike Curves via Election-Methods election-methods@lists.electorama.com wrote:
Once again -- your argumentation is based on the assumption that preferences 46: A, 44: B>C, 10: C are not honest and the "real" preferences are 46: A, 44: B, 10: C. I see no reason for a voting rule to presume that, having only the actual results in hand.
If we’re assuming complete honesty from the voters, score voting becomes optimal almost by definition (or by Harsanyi’s utilitarian theorem). The advantage of median and Condorcet rules is supposed to be better performance if only some voters strategically exaggerate.
Which we should assume from the beginning. Borda's response to Condorcet: "My system is only intended for honest men" is pretty weak. The system should withstand, to the extent possible, contrived voting by dishonest or strategic voters. Because the honest voters are gonna wonder if their 1-point preference of A over B is being swamped by other voters' 5-point preference of B over A. That burden of tactical voting will always exist with a Cardinal ballot whenever there are 3 or more candidates.
The major issue for margins is that, with strategic voters, the election results become effectively random just like for Borda,
No, it isn't. It's purely deterministic measure of counting voters' preference. But the enthusiasm or degree of their preference is not recorded. Only that some number of voters preferred A over B and another number of voters preferred B over A.
Margins proposes that the defeat strength is proportional to both the percent margin and to the size of the election (how many voters weighed in on A and B). Margins is the product of those two measures on how decisive (the % margin) and how important (the number of voters weighing in on the decision) a particular "runoff" between a pair of candidates is.
and even a universally-ranked-last candidate can win.
There has to be at least one ballot with that candidate ranked higher (and one is only sufficient if the vote with the two extreme candidates is exactly evenly split).
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Hi CLC,
The major issue for margins is that, with strategic voters, the election
results become effectively random just like for Borda, and even a
universally-ranked-last candidate can win. The mailing list calls this DH3 and
talks about “burial resistance criteria”, but I find this focus on criteria
instead of specific models of election outcomes kind of silly, so I’ll say it’s
better explained in Burt Monroe’s turkey-raising paper, where he games out
Myerson-Satterthwaite-style equilibria.
I think the key commonality between Borda and margins Condorcet is that the
offensive strategy (burial) looks a lot like a defensive strategy, because
truncation is less convincing as a defense. (Borda may not even provide it.)
In my view, the danger of these methods is not that there is going to be a
coordinated strategy to steal an election, it's that many voters independently
may be unwilling to provide an accurate ranking for the worse of two
frontrunners, assessing that it might give away the election, and possibly
assessing that the other side's voters will be thinking the same way. (If other
voters are burying, then for you to do it too is no crime, it's the defense
available to you.)
If margins elections "go wrong" from time to time, it may encourage more
sincerity, though.
Kevin
votingmethods.net
On 2025-07-01 21:51, robert bristow-johnson via Election-Methods wrote:
and even a universally-ranked-last candidate can win.
There has to be at least one ballot with that candidate ranked
higher (and one is only sufficient if the vote with the two extreme candidates
is exactly evenly split).
I've got the guy plonked, so his message didn't grace my inbox, but I
think he's referring to arguments in the style of Warren Smith's DH3.
One should be careful here, because Warren never proved that every
Condorcet method fails DH3. (And indeed, that is false. Smith,IRV
passes, for instance.) Similarly, he never proved that every pairwise
margins method fails DH3, either. So this statement, if it does indeed
refer to DH3, needs proof - and if it's a blanket statement about every
margins method, it needs a proof that covers every one of them.
-km