Forest, You wrote: > "I wonder if the following Approval Margins Sort (AMS) is equivalent to your Approval Margins method:
1. List the alternatives in order of approval with highest approval at the top of the list. 2. While any adjacent pair of alternatives is out of order pairwise ... among all such pairs swap the members of the pair that differ the least in approval. This method is clone independent and monotonic, and yields a social order that reverses exactly when the ballots are reversed. If AMS and AM are the same, it might be useful to have this alternative description. > AMS is monotonic in a strong sense: if ballots are changed so as to increase alternative X's approval or to give X a victory that it didn't have before, while leaving all of the other approvals and pairwise defeats the same, then X cannot move down in the social order produced by this AMS method. In other words, AMS is monotonic with respect to the entire social order it produces. > After one example it is pretty obvious that AM and AMS are equivalent when there are only three alternatives, since they both yield the CW when there is one, and they both preserve the approval order if the only upward defeat arrow is from the bottom to the top, and they both reverse the closest approval margin pair, otherwise." CB: AMS doesn't seem very "intuitive", especially to the uninitiated, but I like it! (My other worry is that I even understand it.) So how is this method worse than the best of the methods you currently advocate? A perhaps ridiculous question: does the AMS process always stabilize? 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
