Let me answer 2 comments by Markus before getting to the topic in my subject line:
Markus said: Similarily, an election method can only ask about your opinion. And when you answer that you prefer candidate X to candidate Y, then the election method has to make its decision without knowing whether your statement is correct. Actually, whether your statement is correct is of no concern for the election method. I reply: No argument there. I hope I haven't said or implied anything to the contrary. Markus continued: Due to Pattanaik and Peleg, the input of a decision scheme is a set of linear orders. Of course, when you assume that the voters can rank the candidates on the ballot, then you can simply say that the input of a decision scheme is a set of ballots. I reply: Yes, I understand now what they mean, though they don't say what they mean. I understand it only because it's been explained. The input is a set of abstract candidate orderings. A candidate ordering is an abstract thing that isn't necessarily associated with anything physical like a ballot or a voter. As I mentioned to Blake, when P&P call an abstract candidate ordering a "preference", they're using "preference" in a way that's different from its standard accepted meaning. They're using it with a meaning that isn't used outside of their own little culture. Which is their right, of course. But of course this issue of what preference means doesn't affect the matter of whether or not your IIAC is Regularity. Whatever P&P mean by "preference", one thing for sure is that they say "Given the profile of individual preferences...", and you don't say that in your definition. The operative word there is "the". They're saying that there's only one profile of preferences. One set of candidate orderings that doesn't change when we add the new candidate. That's what makes their Regularity very different from your IIAC, as you defined it earlier. I don't think you meant it that way. You intended P&P's Regularity, right? In practice, of course, their abstract meaning for preferences translates, in actual elections, to the candidate orderings on ballots, because of course ballots are the input of the count. Plurality, Approval, RB, & RC pass Regularity so defined. CR fails, because the criterion only talks about order. Maybe they meant: Deleting a loser from the election's ballots and then recounting those ballots should never decrease the win-probability of an undeleted candidate. [end of definition] That sounds like the probabilistic version of my IIAC. Mike Ossipoff _________________________________________________________________ Join the world�s largest e-mail service with MSN Hotmail. http://www.hotmail.com
