Alex: Welcome to the Donald Saari reading club! More comments below.
--- In [EMAIL PROTECTED], "Alex Small" <[EMAIL PROTECTED]> wrote: [...] > So, if you "subtract out" the ballots that form a perfectly symmetric > cycle, Saari has proven that applying the Borda count to what remains will > satisfy the conditions of Arrow's Theorem. In a 3-way race there [...] I must say that your statement of Saari's observation seems a bit misleading, if not inaccurate. Saari shows that the BC is the only positional (or pairwise) voting method which (AUTOMATICALLY) cancels out those symmetrical ballots (reversals and cyclic triplets, in the case of 3 candidates). It is not as if the BC only works if you first cancel out the symmetrical ballots, and then apply it to only the remaining ballots. To the contrary, he shows that all positional and pairwise methods reach the same conclusion when applied only to the ballots which remain (the "perturbation") after that cancellation. That is a very important point, in his view. > The voter profile is in some sense the sum of a symmetric part plus a > perturbation, and the Borda Count satisfies the conditions Arrow's Theorem > when applied to the perturbation. He has also proven that the Borda Count > is the only positional method to satisfy the conditions of Arrow's theorem > when you consider the perturbation. In other words, the only No, not quite. Again, as all methods reach the same outcome when applied to the perturbation, they all would satisfy Arrow's Theorem when applied only to the perturbation (or what Saari calls the "Basic" profile). The important thing is that the BC AUTOMATICALLY cancels out the symmetrical ballots and bases it conclusion on ONLY the remainder. [...] BTW, did you see my review of this book on Amazon.com? Chaotic Elections! : A Mathematician Looks at Voting by Donald G. Saari ; Mass Market Paperback http://www.amazon.com/exec/obidos/ASIN/0821828479/ I hope you will write and publish your own review when you finish it. SB __________________________________________________ Do You Yahoo!? Try FREE Yahoo! Mail - the world's greatest free email! http://mail.yahoo.com/
