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

[robert bristow-johnson]

> On 07/01/2025 3:24 PM EDT Closed Limelike Curves via Election-Methods <election-methods at lists.electorama.com> wrote:
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> > 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.
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> If we’re assuming complete honesty from the voters, score voting becomes optimal almost by definition (or by Harsanyi’s utilitarian theorem). The advantage of median and Condorcet rules is supposed to be better performance if only some voters strategically exaggerate.
> 

Which we should assume from the beginning.  Borda's response to Condorcet: "My system is only intended for honest men" is pretty weak.  The system should withstand, to the extent possible, contrived voting by dishonest or strategic voters.  Because the honest voters are gonna wonder if their 1-point preference of A over B is being swamped by other voters' 5-point preference of B over A.  That burden of tactical voting will always exist with a Cardinal ballot whenever there are 3 or more candidates.

> The major issue for margins is that, with strategic voters, the election results become effectively random just like for Borda,

No, it isn't.  It's purely deterministic measure of counting voters' preference.  But the enthusiasm or degree of their preference is not recorded.  Only that some number of voters preferred A over B and another number of voters preferred B over A.

Margins proposes that the defeat strength is proportional to both the percent margin and to the size of the election (how many voters weighed in on A and B).  Margins is the product of those two measures on how decisive (the % margin) and how important (the  number of voters weighing in on the decision) a particular "runoff" between a pair of candidates is.

> and even a universally-ranked-last candidate can win.

There has to be at least one ballot with that candidate ranked higher (and one is only sufficient if the vote with the two extreme candidates is exactly evenly split).

--

r b-j . _ . _ . _ . _ rbj at audioimagination.com

"Imagination is more important than knowledge."

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