Steve wrote: > What do you think of circular triplets, such as: > > A>B>C > B>C>A > C>A>B, > > and reversals, such as: > > A>B>C > C>B>A. > > If that is all the information that we have to go on (when ordinal preference > ballots are used, it is ), shouldn't either of these profiles cancel out > completely and yield a tie?
Well, yes, when they're taken alone, and any reasonable method would yield a tie in these two elections, although IRV wouldn't in the second. But I don't think that's what Saari is talking about; he thinks adding symmetric groups of votes should never change an election's winner. Adding the second profile will never change the winner of a Condorcet election since it would in effect add 1 to each cell of the pairwise matrix. But say two of the first profile were added to the election 5:A>C>B 4:C>B>A to give 2:A>B>C 5:A>C>B 2:B>C>A 2:C>A>B 4:C>B>A The Condorcet winner changes from A to C. I don't see a paradox here. After all, the votes you're adding may be circular, but they're not entirely symmetric. The added votes in this case have 4 for C over A and only 2 for A over C. I can see how you might intuitively want circular triplets to cancel completely, but is that really a good reason to reject Condorcet methods? Besides, the best Condorcet methods are just as monotonic as Borda. Obviously, if you agree with Saari's criteria, then Borda is for you. I'm not attacking his mathematics, just his criteria. He don't seem to find it important that almost everyone in a well-informed Borda election will benefit from voting insincerely, usually *very* insincerely. Borda works fine in zero-information elections, but how common is it in the real world for no voter to have any clue as to how anyone else will vote? Have you read Blake's arguments against Borda? What do you think of them? ===== Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/honky98/ __________________________________________________ Do You Yahoo!? Yahoo! Sports - Coverage of the 2002 Olympic Games http://sports.yahoo.com
