James, You wrote (beginning with a quote from me): >The AM criterion, on the other hand, is the perfectly >natural putting together of two obviously fundamental >ideas: "that pairwise beaten candidates should tend to >lose" and "that more approved candidates should tend >to win"!
"You mean the "AP criterion", right? "Don't elect a candidate that is pairwise beaten by a more approved candidate." If you want to call it the AM criterion, that's fine, just let me know. But I'm pretty sure that it was the AP criterion last time." CB: Oops! Yes I mean the "Approval Plurality" (AP) criterion. "If you can't keep enough of an open mind to avoid calling my logic "mad", we should probably stop trying to converse on this subject. Maybe sometime you could write a note to me off-list and let me know whence came this impulse to needlessly insult me... as I remember we used to have a rather pleasant and cooperative correspondence." CB: I conceded that the Approval-Weighted Pairwise (AWP) method "has its own mad logic". Someone with a thicker skin might even interpret that as a grudging compliment. Nothing I wrote was meant as an insult to you personally. "What is the logic behind the AP criterion? If A is "more approved" than B, he's probably better, and if A pairwise beats B, he's probably better, so if A is "more approved" then a candidate B whom he pairwise beats, he's definitely better, so why elect B? Is that it? ." CB: Close enough. In election theory, lots of of obvious desirable properties are in contradiction with each other, and we can give very strong objections to most of the simplest proposed rules/standards. We can have a sort of catechism consisting of a probabilistic standard, a strict rule motivated by that standard, and strong objections to that rule. So for example: "More approved candidates should tend to win" suggests "Why not always elect the most approved candidate?" We can answer "If ranking information is also collected, it might reveal that another candidate pairwise beats all the others, and may even be the first preference of more than half the voters"; and we can give the same answer to the question "Why not never elect the least-approved candidate?". Likewise, "Pairwise beaten candidates should tend to lose" prompts the question "Why not never elect a pairwise beaten candidate?". We have the very easy answer that it is possible that all the candidates can be pairwise beaten, and the office needs to be filled. To the question "Why not always elect the most approved candidate whenever all the candidates are pairwise beaten?", our answer is much more complicated (being about strategy) and our objection much weaker. The exasperated questioner (say a potential voter) then says "There must be some simple straight-forward based-on-elementary-principles rule/guarantee that we can have! What about 'never elect a candidate that is pairwise beaten by a more approved candidate'?" I would say "Fine!", and not "When all the candidates are pairwise beaten, we need to determine which of the pairwise defeats is to be over-ridden. James G-A insists that we do that based only on the number of ballots that approve the pairwise winner and not the loser. Your proposed rule is incompatible with that obviously wonderful idea!" While there seems to be no danger at all that the idea that it is acceptable to elect the least approved and pairwise beaten candidate will catch on, I'd prefer to post on things I consider more interesting and important. Chris Benham Find local movie times and trailers on Yahoo! Movies. http://au.movies.yahoo.com ---- Election-methods mailing list - see http://electorama.com/em for list info
