Adam wrote: >It seems clear that only the Condorcet winner (if one exists) will produce >a Nash equilibrium.
Are you suggesting that if there is no Condorcet winner there is no Nash equilibrium, or that if there is a Condorcet winner all of the Nash equilibria will elect the Condorcet winner, or both? The first option is false from what I understand (I thought Nash got his prize and movie for proving that there is always at least one equilibrium, given some very general assumptions). The second seems attractive, and would be a powerful counter-argument to many AV criticisms if true, but I'm not convinced of its veracity. >Although certain dogmatic approaches in approval voting adjustment can >produce a cycle, this doesn't mean a Nash equilibrium does not exist. I understand that there will still be a Nash equilibrium in the presence of a cycle (under certain polling assumptions). I was wondering what the general conditions are (making certain assumptions about voter behavior in the presence of repeated polling) for equilibria where additional polls do not change the outcome. Those equilibria may or may not also be Nash equilibria, since the polling assumptions that I've seen usually assume that people distinguish between the top 2 in revising their strategies. That does not encompass all possible strategic adjustments, however, so it is not entirely clear to me that repeated polling will always find the Nash equilibrium and/or Condorcet winner. I'd like to hope so, however. Anyway, it's an interesting question to explore. Alex
