Forest Simmons wrote: >I must be missing something. Could you give an >example in which the approval winner is not the >winner of the method?
I don't think it's itself a method. It's a "family of voting methods" of them, like he said. The two rules specify what the ballot must look like, and who cannot win. There is a lot of freedom permitted as to who actually wins. To give an example for your question, it would be permissible for a method in the family to elect a candidate who beats pairwise the approval winner. Steve Eppley wrote: >2. For all pairs of candidates, say x & y, y is >socially ordered over x if the number of votes that >rank "y over x" exceeds the number of votes that >rank "x over y" and the number of votes that rank "y >over the dividing line over x" exceeds the number of >votes that rank "x over the dividing line over y." Isn't it superfluous to say "y over the dividing line over x" and vice versa? Won't you get the same results if you say "y over the dividing line" and vice versa? >Assuming only one winner is to be elected, it's >always possible to satisfy condition 2 (or the >revised wording) since the subset of pairings that >meet condition 2 is acyclic. (I have a proof of >acyclicity, but it's tedious so I won't post it >without a request.) I think this is intuitive. Isn't it just a consequence of it being impossible to have a cycle with an approval ballot? >I'm concerned that some voters wouldn't use the >dividing line strategically as intended, and instead >treat it as some sort of "sincere approval" dividing >line. In that case, the dividing line may I believe the method I most recently proposed satisfies your 2nd rule (about who can't win) but not the 1st (about the ballot). That is, it is not possible for a candidate to win if he's beaten by a single candidate on both matrices (Condorcet and Approval). I also think my method could alleviate some of your concern about the voters using the divider efficiently. This is because the voter cannot order among candidates whom they don't approve. Thus if they want to put the "dividing line" (which exists only effectively) right after their first preference, they cannot name compromises. It's debatable whether it would be better to do something other than add the two matrices. >So even though many voting methods could be tweaked >to be in the family that satisfies Sincere Defense, >only the best methods should be considered. I wonder what you think would approach a "best method." Do you think tinkering with the ballot format is completely out? Kevin Venzke [EMAIL PROTECTED] ___________________________________________________________ Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en français ! Yahoo! Mail : http://fr.mail.yahoo.com _______________________________________________ Election-methods mailing list [EMAIL PROTECTED] http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com