[EM] The rationale under the "winning votes" defeat strength measure

[Juho Laatu]

- You could say that the philosophy of margins is to give good results with sincere votes.
- But how about coping with strategic voting?
- The main argument is maybe that in large public real life Condorcet elections it is very difficult to implement and coordinate successful malicious strategies, and therefore one should expect rational voters to vote sincerely.

- You could say that winning votes are intended to cope with threats of some insincere voting scenarios.
- But how about electing the best candidate when votes are sincere?
- A good argument might be that usually there is a Condorcet winner anyway, and if not, most voters tend to rank all major candidates anyway, which makes strange results less likely. Vote truncation for strategic or defensive reasons might be rare. One should also encourage voters not to truncate since we want to get all their preferences, to be able to pick the best winner.

Juho


> On 25. Jun 2025, at 20.02, Toby Pereira via Election-Methods <election-methods at lists.electorama.com> wrote:
> 
> The way I've always seen it is that margins makes more sense from a purely philosophical or mathematical point of view. As Grzegorz alluded to, winning votes can lead to weird discontinuities, and having 50-0 as a "smaller" win than 51-49 seems weird, to say the least. I see winning votes as purely practical and pragmatic. It purely exists because of real-life strategic concerns, not because of any philosophical or mathematical ideal. It's clunky, ugly, and mathematically illogical, but seems to deal with certain situations better than margins.
> 
> Toby
> 
> On Wednesday 25 June 2025 at 17:25:09 BST, Kevin Venzke via Election-Methods <election-methods at lists.electorama.com> 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
> 
> 
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