EM list-- In the _American Political Science Review_, vol. 87, No. 1, page 103 (March 1993), Roger Myerson & Robert Weber published an article as fascinating & compelling as Myerson's article on corruption-encouragement. It's entitled "A atheory of Voting Equilibria". It's best to start with an example. Say the method is Plurality, and the media only devote airtime & printspace to 2 parties, and keep referring to those 2 parties as "The 2 choices". And say people believe that, and vote accordingly. Of course everyone will vote for whichever of those 2 is his favorite, or almost everyone will. The result is easy to predict: Those 2 parties will be the only ones to get any significant number of votes. That will confirm the media's claim that they're the only viable choices. The electorate could be stuck forever on a suboptimal outcome if those aren't really the 2 most preferred parties. We'd never know. Myerson & Weber call that a "voting equilibrium". They point out that, with Plurality, _any_ 2 parties, as long as at least one of them isn't in Condorcet loser position, can win at voting equilibrium, if voters are led to believe that they're the frontrunners. They also point out that, with Approval, if there's a candidate at the voter-median position, he's the only candidate who can win at voting equibrium. A simplified definition of voting equilibrium might be: An outcome, including the officially reported & recorded count results, that is consistent with the prediction(s) that led voters to vote as they did, producing that outcome. It's assumed that everyone believes the same prediction(s), and that everyone votes to get the best outcome for themselves. For this simplified definition, I'd also add that the predictions are certain enough that people feel certain that one candidate-pair is the one that definitely should vote between, but not so certain that the other candidate-pairs have no importance. (Of course with all methods, one votes between more than 1 candidate pair, but only one candidate pair will be the one that is in closest contention, and the one for which you can affect the outcome, if you can affect any outcome). *** Voting Equilibrium Criterion (VEC (tentative)): If candidates & voters are positioned in a 1-dimensional policy-space, where voters prefer near candidates to farther ones, and if there's a candidate at voter-median position, then he should be the only candidate who can win at voting equilibrium. *** Well that's the awkward part, about the certainty of the predictive beliefs. That's the simplification. Myerson & Weber deal with it in a detailed way, which involves the use of candidates' "expected scores". In point systems, of course scoring is simple, and the candidate with highest score wins. They relate the Pij, the frontrunner probabilities, to the expected scores of the candidates. I can't imagine how to apply that to non-point systems, and so I've tried the simplification that I wrote above. Let me know if you notice a problem with it. Especially, let me know if you can improve it. If it seems unsound, then how can it be written more soundly? And how does Condorcet do? My impression is that Condorcet doesn't pass this one, because all rank methods have so many ways things can happen that unintended results can be possible. I don't expect all methods to meet the same criteria, of course. Approval meets some that Condorcet doesn't meet, and Condorcet meets some that Approval doesn't meet. The important thing for me is that both meet a number of important criteria, something that sets them both above all the other methods. Mike Ossipoff ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com
