[EM] Defeat Strength

[Kristofer Munsterhjelm]

On 04.09.2022 21:56, Kevin Venzke wrote:
> Hi,
> 
> I'm afraid that defeat strength is such a tangible concept that it inclines us to view it as
> a finished product that we can now simply customize as we please. Or worse: That we are
> duty-bound to measure it "accurately." We maximize some desired property, readily identified
> within a single pairwise contest, and then apply the minmax algorithm to this ranking, and
> expect it to result in a method whose properties have some kind of relationship to the
> property we were maximizing, or properties that will at least be as good as the defeat
> strength metric sounded.
> 
> I couldn't count how many times I had a nice idea, tried to use minmax or River with it,
> and discovered some horrible basic flaw. Or just mediocre results.

Let's see if I can post to EM again :-) I was having some trouble with 
t-online but it looks like I can at least receive mails again now.

Anyway. I guess there are two ways to answer this kind of question: 
first, we could say "I want to maximize some combination of strategic 
resistance and VSE" and find out where our indifference curve hits the 
Pareto frontier.  Or we could say "this concept is essential to 
democracy as I imagine it and must be present no matter what" (e.g. that 
majority rule must imply Condorcet).

I'd say that for defeat strength, I can't see any obvious second-type 
argument that say, margins or wv naturally generalize democracy and so 
must be present. Statistical models would disagree, too: if 
bottom-ranking is considered to be the voter saying "I don't know where 
to rank these candidates", that's a different thing to the voter 
implicitly intending to bottom-rank every nonranked candidate.

I tend to personally favor wv, but that's partly due to convention, 
partly due to strategy resistance.

(Now that I think about it, I guess there's a third category: that 
algorithm feature X should be present because it seems natural to the 
voters, or that Y shouldn't because it seems to arrive at a conclusion, 
even if it's a correct one, as by magic, and so won't be considered 
legitimate by the voters.

Again there would be two perspectives: a relative one where this much 
strategy resistance or VSE can make up for an incomprehensible 
algorithm, and an absolute one where there's some level of complexity 
the voters simply won't accept.)

-km