James, I'd written: >One of the original justifications of the Plurality >criterion was about inferring (conservatively) >approval from rankings.
And you responded: > This can't be done. That is not the only or my favourite justification, but don't you think its reasonable to assume that voters "approve" the candidate they rank in first place and not those they rank equal-last? You wrote (Sat.Apr.10): "Chris: > >I find the phrase "defeats consisting of..." an odd >formulation with an unclear meaning. Arguably "defeat" >is just a label for a result which just is, and so >doesn't really "consist of" anything. Would the word "include" be more grammatical in place of "consist of"?" CB: Not really. It is possible to have an unclear meaning without being ungrammatical. You continued: "Let me clarify my criterion. To keep things simple, I'll call it the approval weighted pairwise (AWP) criterion, since it's obviously designed just to support AWP. Here's the definition: "A voter expresses a strong preference for X over Y if the voter approves X but not Y. If A pairwise beats B, and there is no beatpath from B to A such that each defeat includes as many or more strong preferences than the A>B preference, then B shouldn't win." " CB: I think you need to specify "..strong preferences on the winning side". >Maybe AWP is a bit more strategy resistant than AP, I think that it is more than "a bit". >but only at the huge cost of flouting AP. Your examples of AWP resisting strategy better than AP have not been very impressive to me (or I gather,Ted). "I could just as easily say that AM and DMC have a huge cost in that they flout the AWP criterion." CB: Not with any credibility, since the AWP criterion was "obviously designed just to support" the method (as you put it); and it doesn't seem to test for anything that anyone was worrying about before the method was invented. 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"! I concede that the AWP method has its own mad logic, and that it succeeds somewhat at what it tries to do. (And you can take that as my general reply to all those arguments of yours that you complain that I "haven't replied to".) But I think a lot of voters wouldn't understand the AWP method or criterion, and some or many of those that do wouldn't be greatly reassured by the criterion. On the other hand, I think most of the voters would understand and appreciate the AP criterion, and meeting it means that we always have some very simple and effective retort to potential complainers. Regarding your example: 26: B>>D>K 22: B>>K>D 19: D>K>>B 6: D>>K>B 22: K>D>>B 5: K>>B>D You wrote: "By the way, if AWP elects Kerry, the Dean voters (who by your logic have a huge and unanswerable complaint) will not be interested in arguing for your AM method, because it results in the election of Bush." CB: No, but here the Dean voters can argue for DMC or Approval Elimination. The 6 D>>K>B voters might think that AM would give their candidate a better chance next time (I suppose assuming they think that the 26 B>>D>K voters are sincere). 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