[EM] The "Single Contest" method

[Kevin Venzke]

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.

[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.

Thanks.

Kevin Venzke