[EM] Defeat Strength

[Kevin Venzke]

Hi Kristofer,

>> 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.

> 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 like to keep as few as possible of the second type of opinion.

> 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.

Though, I think such an opinion could be possible. If you take specific method properties as
axiomatic you could significantly constrain the available choices.

> 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.

>From the standpoint of minimizing incentives, there is a similarity between these two: No
voter obtains a complaint or an incentive over preferences they didn't have. (This is where
symmetric completion hurts the performance, as we may yield to claims that are
hypothetical.) I'm not sure how to see a difference in implication between "I meant them to
be equal" or "I didn't know the relative order." Maybe an estimate of social utility
would vary based on how voted indifference is interpreted?

> 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.)

"Marketability" I certainly acknowledge as a thing. Hopefully it doesn't force too many
decisions, and hopefully marketability isn't mistaken for more fundamental merit.

I'm not completely sure what is the accepted way to determine VSE. Is this the same as the
principle that a voter's zero info strategy is to submit a complete sincere ranking? I feel
like that principle lies more on the marketability side, since it shouldn't be a realistic
scenario.

Kevin
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