Hallo, Kristofer Munsterhjelm wrote (2 May 2010):
> Perhaps there's a better method still than Kemeny, > say a method that is at least as good on average > and satisfies clone independence (or perhaps IPDA, > etc). My aim was to find an election method that is cloneproof and that usually produces winners with weak worst defeats. I believe that the maximum, that you could ask for, is that the winner is always chosen from the "MinMax set". See section 9.1 of my paper: http://m-schulze.webhop.net/schulze1.pdf In section 3.6.1, the MinMax set is {A,C,D}. However, when we add the Pareto-dominated candidate E, then the MinMax set is {B}. This demonstrated that IPDA and the desideratum that the winner is always chosen from the MinMax set are incompatible. ********* Kristofer Munsterhjelm wrote (2 May 2010): > That would be Condorcet with dual dropping, and the > organization is the MKM-IG: http://www.mkm-ig.org/ > I think Schulze said the method might not necessarily > be cloneproof: the idea would be something like that > in the base scenario, the Schulze winner is best, but > then, when you introduce (or remove) a few clones, > the Tideman winner becomes "better" and so it switches. I believe that this method also might not necessarily be monotonic. Example: Candidate A is the Schulze winner. Candidate B is the Tideman winner. Condorcet with dual dropping chooses candidate A. Suppose some voters rank candidate A higher. Then, as the Schulze method is monotonic, candidate A is still the Schulze winner. However, it is possible that the Tideman winner is changed from candidate B to some other candidate C and that Condorcet with dual dropping chooses candidate C. Markus Schulze ---- Election-Methods mailing list - see http://electorama.com/em for list info
