Steph-- You wrote: To Mike Ossipoff... I find some of your criterias partially subjective. Please let me explain. If a voter decides to truncate its preferences, he changes some of his pairwise opinions from A>B to A?B (meaning he does not care anymore). It seems to me reasonable to accept that a change in ballots can then imply a change in A or B's support. I reply: Sure, and that's true with any method, including the ones that meet GSFC. GSFC doesn't prevent loss of support from being counted. You continued: Hence if C was the winner, but A or B's support growths enough without changing C's support It seems acceptable that C could loose his winner status. I reply: Certainly, and that happens with GSFC complying methods too. GSFC & SFC don't actually mention truncation, but invulnerability trunation has usually been defined to mean that truncation can't steal the election from a well-supported CW. But SFC & GSFC, as I was saying, don't mention truncation, and are instead more general. They merely say that, without falsification of preferences, no one should win who has a sincere Smith set member preferred to him by a majority who vote sincerely. (no one, that is, who isn't a member of the sincere Smith set). That's a reasonable thing to ask for. It's reasonable for the winner to come from the sincere Smith set, and if that candidate is well supported against someone else, it's reasonable that that other candidate shouldn't win. The important thing about GSFC is that it doesn't specify that anyone uses defensive strategy, and so complying methods have GSFC's guarantee even if that majority doesn't use any strategy, or do other than vote sincerely. That's why it's called the Strategy-Free Criterion. It talks about a plausible conditions under which complying methods are strategy-free. That's what I most like about the Condorcet(wv) versions. You continued: SPC (secret preferences criteria) should ask for C's support invariance by any change in the pairwise comparison between A and B, not for C's status immuability. I reply: That would be a different criterion, but GSFC doesn't ask for anything unreasonable. The SPC that you describe sounds similar to IIAC, Heritage, & Regularity, criteria met by Approval, but not by any rank method that I know of. With rank methods, deleting a candidate from the ballots, and recounting the ballots, can reduce the win-probability of an undeleted candidate. Though A initially wins, deleting C can cause A to lose to B. That won't happen in Approval. Steph. _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
