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<div dir="ltr" data-setdir="false">The way I've always seen it is that margins makes more sense from a purely philosophical or mathematical point of view. As <span><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">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.</span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(38, 40, 42); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">Toby</span></span></div><div><br></div>
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On Wednesday 25 June 2025 at 17:25:09 BST, Kevin Venzke via Election-Methods <election-methods@lists.electorama.com> wrote:
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<div><div dir="ltr">Hi Grzegorz,<br clear="none"><br clear="none">> 1. What exactly are the axioms that Condorcet rules with WV satisfy, but with<br clear="none">> margins do not? (I'm only aware of the Plurality criterion)<br clear="none"><br clear="none">Very few have been articulated, but:<br clear="none"><br clear="none">> 2. I have sometimes read that WV are better to prevent strategic behavior of<br clear="none">> the voters (without much details),<br clear="none"><br clear="none">I do use the minimal defense criterion, which represents the notion that a full<br clear="none">majority of voters can always get their way if they want to, so it will reduce<br clear="none">compromise strategy for the majority if you just give them their way when you<br clear="none">know what it is.<br clear="none"><br clear="none">To me, WV resolution is an approximation of an ideal. I made a webpage that<br clear="none">attempts to show what options are available for electing from a provided cycle,<br clear="none">with the aim of avoiding compromise incentive when you can:<br clear="none"><br clear="none"><a shape="rect" href="https://votingmethods.net/check" rel="nofollow" target="_blank">https://votingmethods.net/check</a><br clear="none"><br clear="none">This doesn't always favor WV, and sometimes there are no actual solutions.<br clear="none"><br clear="none">> but do you have any idea how to justify WV<br clear="none">> more "intuitively" or "philosophically", assuming sincere votes? Margins are<br clear="none">> very easy to justify. I came up with two possible justifications for WV here<br clear="none">> (described below), but I'm not sure how convincing they could be for the<br clear="none">> general audience.<br clear="none"><br clear="none">Here I'm not sure. I guess by "sincere votes" you mean that absence of a<br clear="none">pairwise preference indicates an expression that two candidates are equal. Or<br clear="none">maybe that truncation is not different from explicit equal ranking.<br clear="none"><br clear="none">> 3. Don't you think it is "ugly" that the WV measure applied e.g., to Schulze<br clear="none">> or RP/MAM requires us to artificially exclude "50% vs. 50%" ties between<br clear="none">> candidates from consideration (or equivalently, to mark them as the weakest)<br clear="none"><br clear="none">That's never occurred to me actually. All non-wins are excluded from<br clear="none">consideration.<br clear="none"><br clear="none">> --- and that a victory "50%+1 vs. 50%-1" is rapidly considered to be quite<br clear="none">> strong, stronger than e.g., a "45% vs. 1%" victory (with 54% voters who rank<br clear="none">> both candidates equally)? Under margins, ties or close ties are naturally<br clear="none">> considered the weakest. How would you refute this argument?<br clear="none"><br clear="none">Ideally by some kind of rephrasing. I don't know if this is possible, but it<br clear="none">would be nice if the matter could be presented without making it feel like the<br clear="none">defeats themselves have an interest in being respected.<br clear="none"><br clear="none">Alternatively, you want to find a explanation where losing votes are just<br clear="none">meaningless, because for the practical purposes (the strategic incentive ones),<br clear="none">they are. You don't obtain a valid complaint against the method by losing a<br clear="none">close race, you can only get one by winning races and losing anyway because you<br clear="none">didn't lie.<br clear="none"><br clear="none">(In a 51:49 matchup, those on the losing side have no power to lie and change<br clear="none">the outcome (we hope), while there is considerable possibility that those on the<br clear="none">51 side *could* lie and win (i.e. if they had not), because they comprise more<br clear="none">than half the voters. With 45:1, there are decent odds that those on the 45%<br clear="none">side could win by lying; your method could determine this to be sure, if you<br clear="none">wanted, before ruling for instance that 45:1 prevails over a win of 40:39. WV is<br clear="none">just making a mathematically easy "best guess.")<br clear="none"><br clear="none">> Regarding pt. 2, here are my ideas for a high-level intuitive principle behind<br clear="none">> WV:<br clear="none">> (1) "It is much harder (infinitely harder?) to convince a voter to change his<br clear="none">> mind from B<A to A>B, than it is to change his mind from A=B to A>B". Then, in<br clear="none">> particular, it is more probable that a "45% vs. 1%" victory would become a<br clear="none">> "45% vs. 55%" defeat, than that a "51% vs. 49%" victory would become a defeat.<br clear="none"><br clear="none">That has some familiarity to me. If the winning side has a full majority then we<br clear="none">"know" it is right. In fact if you entertain the concept of an overall "median<br clear="none">voter" it suggests to us something about what that voter thinks.<br clear="none"><br clear="none">Though I understand that you want to suppose that the equalities are in fact<br clear="none">sincere.<br clear="none"><br clear="none">In that case, if it's 45% A>B, 54% A=B, 1% B>A, my observation would be that the<br clear="none">median position is that A and B are equal. The 54% aren't just abstaining, are<br clear="none">they? I don't think that's what the assumption of sincerity implies.<br clear="none"><br clear="none">Your second idea is kind of suggestive of this actually... You're just focusing<br clear="none">more on voters' desire for how the matchup is handled.<br clear="none"><br clear="none">> (2) "If a voter votes for A=B, then he is not neutral, but he is actively<br clear="none">> voting against treating the resolution of the matchup between A and B as<br clear="none">> important". Then, in particular, in the case of a "45% vs. 1%" victory, we in<br clear="none">> fact have 45% of voters who consider it important to resolve the matchup in a<br clear="none">> particular direction, and 55% of voters who think otherwise. This is a smaller<br clear="none">> number than for a "51% vs. 49%" victory.<br clear="none"><br clear="none">I view this possibility of voters having such a sentiment, and acting on it in<br clear="none">this way, more as something useful that WV enables. I don't think we can say<br clear="none">it's intuitively the case that voters are meaning to do this.<br clear="none"><br clear="none">Kevin<br clear="none">votingmethods.net<div class="ydp5f2706ffyqt6650537486" id="ydp5f2706ffyqtfd40143"><br clear="none"><br clear="none">----<br clear="none">Election-Methods mailing list - see <a shape="rect" href="https://electorama.com/em" rel="nofollow" target="_blank">https://electorama.com/em</a> for list info<br clear="none"></div></div></div>
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