[EM] The rationale under the "winning votes" defeat strength measure
Chris Benham
cbenhamau at yahoo.com.au
Sun Jun 29 21:59:54 PDT 2025
>
> 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 at 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 at 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 at 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,
>>> >
>>> >> 1. 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:
>>> >
>>> >> 2. 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.
>>> >
>>> >> 3. 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 - seehttps://electorama.com/em for list info
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