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

[Chris Benham]

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
>
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