Warren Smith wrote: >... > Well, one reply to that is "duh." Another reply is, there are matrices > which do not arise from ballots. It is an interesting question which > matrices are achievable and which are not. > > Bishop's algoorithm if it works (which I doubt) would answer that question. > I have a method involving solving an integer program which does answer the > question, but only at heavy computational cost. Bishop's method > if it works would have mild computational cost. > My method works and I doubt Bishop's works, but it would be nice > to produce an explicit counterexample to Bishop's algorithm.
I think I've found one: A B C D A - 0 0 1 B 3 - 1 2 C 3 2 - 3 D 2 1 0 - This is a valid Condorcet matrix, created by the ballots C>B>A>D, C>D>B>A, and B>C>D>A. My CMD proposal creates two C>B>D>A ballots, which would force the remaining ballot to contain a cycle. ---- election-methods mailing list - see http://electorama.com/em for list info
