[EM] Approval Equilibria

[Forest Simmons]

On Mon, 6 Oct 2003, Forest Simmons wrote:

<snip>

> Now let g(x)=max(0,x-z) where z is the largest whole number such that the
> corresponding G=g(F) has a non-zero equilibrium vector W.
>
> This equilibrium corresponds to the rule ... pick the winning candidate by
> randomly drawing a ball from a bag which has zero balls for candidates
> with fewer than z approval votes, and has c-z balls for each candidate
> with approval count c.
>
> It turns out that if there is a Condorcet Winner, then the highest z value
> will be sufficient to filter out all of the other candidates.  Only the CW
> will have higher approval than z, so the CW has all of the balls in the
> bag, and wins with certainty.
>
> If there is no CW, then some other candidate or set of candidates may have
> positive probability as well.
>

The method that I have nick named "Auntie" is an approximate algorithm for
finding this highest possible z, and then awarding the win to the
candidate with the greatest number of balls in the bag, instead of going
through with the drawing.


We could decrease the (already low) manipulability of "Auntie" by doing
the drawing in the case of two or more candidates with more than z
approval.

Forest