[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 :
> >>[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.)
>

Yes. Of course you can go the other way around, too: for each threshold, try
every 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.


Can you explain further? I don't see how it has any non-semi-honest
incentive at all. Perhaps it does have a bullet incentive, though.


> Maybe one
> could just look at U (like SC does).
>

But then the threshold is always pushed down.

How about maximizing D(A) * (D(A) + D(B))? Or D(A) * (D(A) + D(B) + M),
which is the same as D(A) * (V-U)?


> 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
>
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