[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 :
>>[begin quote]
>>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.

What puzzles me is that I don't know how to pick the pair without
knowing the threshold. Yet the reverse seems true also.

I *think* this is what you do, or can do:

For each pair, find the best possible score this pair could have by
moving the threshold. (So, for each pair you try every threshold. The
best score ever achieved indicates the winning pair.)

I did an example on paper. In my example the "M" score was almost
always zero, which makes me doubt the M*U product will work well in
sims. Also, disfavoring a high M score has an obvious favorite 
betrayal incentive which (at least in SC) is noticeable. Maybe one
could just look at U (like SC does).

In my example the threshold made no difference, as the same pair would
win. So, if I were just picking the pair which can get the best score
one way or another, I would dodge the question of how to break ties
between two thresholds.

Kevin Venzke