On Fri, 05 Nov 2004 11:30:05 -0800, Steve Eppley <[EMAIL PROTECTED]> wrote: > Paul C asked: > > Does Eppley still read this list? > > Yes, sometimes. By the way, I prefer that my friends > call me Steve.
Steve it is. > I chose the tiebreaker for complete satisfaction of clone > independence, monotonicity and strong Pareto. My current method is definitely not clone independent. But that raises a question Is clone independence strictly more important than determinism? I've defined a variant of my method which is strictly more deterministic than MAM and retains clone independence (and all the properties I've already proven for my original method, like monotonicity and strict Pareto). The variant is also strictly less deterministic than my original proposal. By "strictly more deterministic" I mean that the deterministic ballot sets for my variant are a strict superset of MAM's deterministic ballot sets, where a deterministic ballot set is a ballot set where the voting method chooses a particular ranking with probability 1. I'll describe the variant in a later post if people are interested; what I'm interested in at the moment is whether people would consider it to be an improvement given the properties listed here. Where the variant is deterministic, it always makes the same decision as my original method. But where it is nondeterministic, my original method would have sacrificed clone independence to deterministically choose one of the winners Consider these ballots 10 A > B1> B2 10 B1> B2 > C 10 C > A where we consider B1, B2 to be clones. With the variant, A and C have a 1/3 chance of winning, just as if the clones are not present. The original treats the clones as "extra information" used to resolve ties, and declares A > B1 > B2 > C the winner. Is that desirable behaviour? Is it thought likely that supporters of A would anticipate the tied circular ranking, and strategically nominate a clone of B to break the circular rank, and fool voters into ranking B1 and B2 together even though B2 is really sponsored by an A supporter? Or is it better, where there would otherwise be a nondeterministically resolved tie, to say that if A does better than two alternatives and both alternatives do better than C then that's enough information to resolve the tie in favour of A > B1 > B2 > C? -- __ \/ o\ Paul Crowley /\__/ www.ciphergoth.org ---- Election-methods mailing list - see http://electorama.com/em for list info