EM list: A few comments on Saari's letter: Saari says that Copeland with 3 candidates doesn't have strategy problems as described by Gibbard & Satterthwaite. Copeland with 3 candidates, when there isn't a candidate who beats each one of the others, doesn't return a winner. *** Saari says that he can say that any method is "best", by a suitable choice of criteria. Then later he says that a version of Borda is the theoretical best :-) Even theoretically, there's no "best", except based on some particular standard(s). Maybe by Saari's theory of symmetries Borda is the theoretical best. Sorry, that doesn't make the unqualified theoretical best. *** Saari says that the methods that always elect a majority winner (candidate who beats all the others pairwise?) if there is one must violate a certain kind of symmetry, and that a consequence of that is that those methods have a high probability of electing a Condorcet loser. Wrong. The better Condorcet versions never elect a Condorcet loser. It's good to find out about methods before telling about their properties. *** Saari says that Borda can be modified to handle its difficulties. How would he modify it so that a voter could have all of his expressed preferences fully-counted? How would he modify it to meet the defensive strategy criteria? Or to not violate majority rule worse than Plurality does? Speaking of the wish to have all of one's preferences fully & reliably counted, a basic goal of rank-balloting, Borda only lets you have _one_ pairwise preference fully-counted-- the preference for your voted 1st choice over your voted last choice (unless you divide one of those rank positions between more than 1 candidate, in which case none of your preferences are fully-counted). By "fully-counted", I mean counted at full- strength, maximum strength. Counted as strongly as any other preference vote of anyone else. That's a rhetorical question, because Saari doesn't participate in this list. No problem. If his proposals ever become actual public proposals, then we can deal with them at that time, and they won't withstand public scrutiny. *** Mike Ossipoff ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com
