On Tue, Sep 13, 2005 at 09:45:12AM +0200, Jobst Heitzig wrote: > > Dear Andrew and Stephane! > > Andrew wrote: > > Actually even this weaker claim (as I understand it) is wrong. Consider the > > following election with 100 voters: > > > > 23 A>B>C > > 25 A>C>B > > 3 B>A>C > > 26 B>C>A > > 3 C>A>B > > 20 C>B>A > > > > Therefore we have A preferred to B 51-49, A preferred to C 51-49, and B > > preferred to C 52-48. So A is a strong Condorcet winner. But consider what > > happens when the 3 B>A>C voters decide to bury A, changing their ballots > > to B>C>A. Then a cycle results: > > > > A vs. B: 51-49 > > B vs. C: 52-48 > > C vs. A: 52-48 > > > > According to all wv methods, we drop the weaker A vs. B preference, and B > > wins. > > In DMC, those who prefer A to B can easily protect the A>B defeat by placing > their approval cutoff between these two candidates: > > 23 A>>B>C > 25 A>>C>B > 03 B>A>C, whatever approval cutoff > 26 B>C>A, whatever approval cutoff > 03 C>A>>B > 20 C>B>A, whatever approval cutoff > > Same cycle A>B>C>A, approval scores A>50>B, hence B is doubly defeated by A > and thus loses in DMC. In view of this counterstrategy, it makes no sense for > the B voters to bury A. > > Yours, Jobst
But note that this depends on the C voters placing *their* approval cutoff lower. And the election's close enough that they may not know whether to defend A against B or C against B. Defense seems pretty difficult to me. Here are a couple of (more extreme) examples to think about that produce the same cycle and strategic vulnerability: 48 A>B>C 3 B>A>C 1 B>C>A 3 C>A>B 45 C>B>A 3 A>B>C 45 A>C>B 3 B>A>C 46 B>C>A 3 C>A>B In the first case, B is able to swing the election even though only 4 voters have B as a first choice. In the second case, the presence of C enables B to swing the election even though the 3% who prefer C like A more than B. -- Andrew ---- Election-methods mailing list - see http://electorama.com/em for list info
