[EM] Equilibrium in Approval Voting

[Alex Small]

Adam wrote:

>I say it's an equilibrium because nobody has any reason to regret the way
>they voted. I would suppose (although I have seen no proof of it) that
>such an equilibrium can only exist for the sincere Condorcet winner.

I'm just an amateur, but isn't an Approval election just a game in which
every player has a finite set of strategies, and payoffs for each
strategy?  If so, then doesn't it have to have a Nash equilibrium?

A separate question is equilibrium under repeated polling.  Brams and
Fishburn show with examples that if after each poll people adjust their
strategies to vote for their favorite of the top 2 (as well as any whom
they prefer to him, and any candidate they rank between the top 2 whom they
consider acceptable) cycles can occur.  e.g. First A and B are contenders,
after adjustments A and C are, after more adjustments B and C are, and
finally it's back to A vs. B.  They didn't lay out any general conditions
for cycles, however.

Alex