Ted, In this example of James G-A's: Preferences 26: A>>C>B 22: A>>B>C 19: C>B>>A 06: C>>B>A 22: B>C>>A 05: B>>A>C
Direction of defeats A>C 52-48 C>B 51-49 B>A 52-48 Approvals: A48, B46, C47. Originally, A was "Bush", B was "Kerry" and C was "Dean"; and the 26 A>>C>B voters were presumed to be Burying B (i.e., sincere was A>>B>C). You wrote (Thur.Apr.28): >What happens if the 22 B>C>>A voters move the approval cutoff upward, >to get > > 22: B>>C>A > >You get > > Approvals: A48, B46, C25. > >Consider the pairwise array with approval on the diagonal: > > A B C > A 48 48 52 > B 52 46 49 > C 48 51 25 > >B is now the DMC (and MRAV/AM) winner. > >Even if the 19: C>B>>A voters moved their cutoff up >as well, B would still win. > >This illustrates a Later-no-harm violation of the >approval cutoff inDMC/AM: B- and C-preferring voters >actually get the better effect of defeating A if they >do NOT approve each other. CB: Presumably you meant to write that those anti-A voters *can* "actually get the better effect of defeating A etc." because you also wrote: >B would also have been elected if the "6: C>>B>A" >voters had moved their cutoff below B. > Leaving aside for the time being what we call it, the property/criterion I think you are referring to could be defined thus: "If x wins, and afterwards some identical ballots that approve x are uniformly changed only so that they approve more candidates than previously; then if there is a new winner it must be one of the candidates approved on these altered ballots." Does AWP meet this? (James?). 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
