Markus wrote:
An election method violates "Independence from Irrelevant Alternatives" when there are situations where you can increase the winning probability of a given already running candidate by introducing an additional candidate. An election method violates "Independence from Clones" when there are situations where you can (1) increase or decrease the probability that a candidate of a given set of clones is elected by introducing additional clones to this set of clones or (2) increase or decrease the probability that a given candidate is elected by introducing additional clones to a set of clones to which this candidate doesn't belong. I reply: Then your definitions of those 2 criteria don't make any stipulations about how people vote? They don't have to vote sincerely, for instance? Or, if they have to vote sincerely, then what definition of sincere voting is used? Does Approval pass your IIAC? Your ICC? If a stipulation about how people vote isn't added to your IIAC definition, then what method passes it? What method passes your ICC, copied above, if no stipulation about how people vote is added to it? Some of us agreed that ICC seems to work as expected when sincere voting is stipulated, and clones defined in terms of sincere preferences. That's also true of the Condorcet Criterion, by the way. I've heard lots of definitions of IIAC, most or all incomplete. If anyone knows how Arrow himself defined it, could they post an English translation of it? I state it in terms of actual votes: Deleting a loser from the ballots and recounting those ballots should never change who wins. [end of definition] But I don't claim that that correctly represent's Arrow's IIAC. Mike Ossipoff _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com
