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

[Grzegorz Pierczyński]

Hello,

I have a question regarding defeat strength measures. I observed that most
voting rules researchers prefer the "winning votes" (WV) measure to
"margins". In particular, to my knowledge, all real-life implementations of
Schulze use this measure. Since I'm thinking of engaging in promoting
Condorcet methods in my country, I'd like to better understand the
arguments behind this opinion. In particular:

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)

2. I have sometimes read that WV are better to prevent strategic behavior
of the voters (without much details), 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.

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) --- 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?

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.
(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.

Curious to hear your ideas.

Best,
Grzegorz
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