[EM] Defeat Strength

[Forest Simmons]

It seems strange to me that many voters believe "one person, one vote" to
mean that their vote is simply their only (or first, in case of rankings)
preference, which cannot change, unless nobody has more than half of the
"votes", in which case there can be a runoff, instant or otherwise.

Martin Harper saw that mindset, and in response proposed a final step in
Approval, analogous to the one and only head-head step of IRV, to determine
which of the candidates got your actual vote:

The candidate that ends up with your actual vote is the unique candidate,
among those you marked as approved, that got the most total approval from
the other ballots.

This step merely confirms the winner without changing it ... so is
functionally superfluous... except for promoting the peace of mind of the
voters worried about the "actual votes", as opposed to approval counts.

If you combine Martin Harper's definition of "actual vote" with Michael
Ossipoff's basic approval strategy, you will find that the "actual"
Approval vote of a rational voter V with complete information, goes to the
same candidate that V would vote for in a Plurality election.

The functional advantage of Approval over Plurality is that it is
robust.... unlike Plurality it has a built in safety net ... many intuitive
strategies that do not depend on complete information are quite close to
optimal.

Think of Ossipoff's strategy: approve every candidate you like at least as
well as your most prudent Plurality choice X (sacrificing Favorite F for
Compromise C if you think that is neccessary for the best expected outcome).

You can see that Plurality is precarious compared to Approval, but (it
turns out that) with completely informed sophisticated voters, both methods
elect the same candidate.

Approving not only X, but also everybody you like more than X, is a
statistical safety net that tends to cancel out many judgment errors ...
inevitable errors in practice, because of degrees of misinformation and
strategical naïveté.

So in practice, the candidate approved by the most voters is the one that
well informed prudent voters would elect if they could only "choose one."

A better known, less demanding (in terms of information) Approval strategy
is to approve all candidates down to the one K most likely to win ...
inclusive, if you prefer K to the apparent runner up J.

If everybody uses this strategy the winner will either be the pairwise
choice between K and J, or somebody that defeats the projected winner K
pairwise ... someone with popularity underestimated by the public polls.

Someday, in the remote future, voters may be comfortable thinking of a
vote  as (for example) a point representing an alternative in some
candidate/issue space. In that context, the winning position may be defined
as the one "most central" to the collection of votes (ballot points
submitted). One method of this type differs from another according to the
measure of "centrality."

What can we do to promote a broader view?

-Forest


On Tue, Sep 6, 2022, 1:19 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> 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
>
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