[EM] The "Single Contest" method

[Jameson Quinn]

2011/7/21 Kevin Venzke <stepjak at yahoo.fr>

> Hi Jameson,
>
> --- En date de : Jeu 21.7.11, Jameson Quinn <jameson.quinn at gmail.com> a
> écrit :
> >>By "meaningful" you don't mean "sincere" or something do you?
> >
> >Well... sorta. More like "anchored by sincerity". The point is that
> >with real voters, if strategic pressure isn't too strong, the median
> >will stay at some predictable place, which then can be used for
> >others' strategy. With simulated voters, the smallest strategic
> >pressure, or even a random walk, will eventually push the median to
> >max or min rating, and then the method loses its power of
> >discrimination.
> >
> >So I'm not hoping that everyone will be "sincere", I'm just positing
> >that "sincere" should have some meaning which voters can fall back
> >on if there isn't any particular strategic reason not to. This is
> >similar to Balinski and Laraki's insistence on "common terminology
> >of judgment", which they spend several chapters of their book
> >discussing.
>
> Oh, I see. I guess I'm not sure how common this kind of situation
> would be in a public election. For some candidates I will always want
> to vote in a strategic fashion, and it feels odd to me to consider
> voting other candidates in a sincere fashion right on the same ballot.
>

Yes, but in many cases, you can be "strategic" without too much distortion.
For instance, if you are strategically voting A>B, or A>cutoff, that does
not mean that you must push A to the top rank, if there is a predictable
cutoff; but if there are no "sincere anchors" for other voters, it probably
does.


>
> [begin quote]
> Let me be define the terms. If the pair with the greatest approval
> coverage is A and B, then "approval-decisive votes for A" D(A,X) at
> threshold X means the absolute number of ballots with A above X and
> B below X. The "mutual approval" M(X) is the number of ballots which
> approve both A and B; and the "mutual disapproval" U(X) is the
> ballots which disapprove both. Possible cutoff metrics to maximize:
>
> D(A,X) + D(B,X) : (what I suggested) On second thought, this could
> elect the guy who most thoroughly beats Hitler.
> D(A,X) * D(B,X) : Avoids the problem above, but too much of a focus
> on "contested" results, whether or not these are majority results
> min(D(A,X), D(B,X)) : like the previous, but worse
> -max(M(X), U(X)): this looks good to me. Unlike the metric I first
> suggested, this does target some form of "median" for the cutoff.
> -(M(X) * U(X)): Similar to the previous
>
> So, I guess I'm saying, instead of maximizing the approval-decisive
> votes, minimize the max of (the mutual approvals or the mutual
> disapprovals). Or perhaps their product.
> [end quote]
>
> Just to be clear, you're saying one selects the cutoff (which will
> be uniform across all ballots) such that it maximizes/minimizes a
> certain score for any pair of candidates. That's what makes sense to
> me as I'm thinking about this. But let me know if it's wrong.
>

Almost. So that it maximizes / minimizes the score for the pair of
candidates selected for the the Single Contest. Although setting it so that
it maximizes/minimizes for any pair is also feasible, and might work well.

JQ
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