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
