[EM] Defeat Strength

[Forest Simmons]

As I understand it, the custom of treating truncation/abstention the same
as equal last rank is a practical expedient to ward off dark horse upsets.

On Fri, Sep 9, 2022, 2:31 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 9/9/22 07:12, Kevin Venzke wrote:
> > 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?
>
> For truncation in particular, I think equal last means that unranked
> candidates provides information to the method that the voter desired
> those candidates to be considered worse than everybody else, while "I
> don't know" indicates that the voting method shouldn't care at all.
>
> As an extreme example of the distinction, I once visited a web site
> called "kitten duel" or something (it's no longer up), where the site
> would show you two kitten pictures side by side and ask you which is
> cutest. Suppose that there was such a kitten duel site with persistent
> identities. Then if I visit it while logged in and choose the left
> picture, that means I prefer the picture on the left to the right, but
> it doesn't mean that I consider every other kitten picture to be
> equal-ranked for worst. I just haven't been asked, so the method doesn't
> know. It's the difference between my contribution to the Condorcet
> matrix having 0 everywhere not explicitly 1, and having "?" or "N/A"
> everywhere but in two cells.
>
> >> 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.
>
> VSE is roughly speaking expected normalized honest performance under
> some model. You create a number of synthetic voters whose utilities you
> know, have them vote honestly, and check the utility of the winner
> relative to random ballot (on the one hand) and the highest utility
> candidate (on the other).
>
> There's a trade-off between honest performance and strategic resistance
> that creates a Pareto frontier - more of one leads to less of the other
> if your methods are perfectly efficient.
>
> For instance, Random Ballot is entirely strategy-proof but has a nonzero
> probability of electing a candidate that everybody but a single voter
> ranks last, and thus has pretty bad honest performance. On the other
> hand, Borda tends to do well under honesty but has serious strategy
> problems.
>
> -km
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