Good catch. Of course, this means that there must be more than 3 members of the Smith set, as well as some other conditions (generally, of the voters who consider A as neither worst nor best of the original Smith set, a larger or "stronger" group must consider B as last than the group which considers B as first; so this limits the number of voters who could see non-monotonic results).
So you're right. Score DSV is only monotonic up to 3 (serious) candidates. Make that 4 if you use the Dutta set (which cannot have 4 members) instead of the Smith set. That is a better system generally except that it's more of a pain to explain. Still, you've pointed to a clear advantage for Schulze. So, how do you respond to the two things I see as clear advantages for Score DSV over Schulze: the "defensive participation criterion" (*If a given election chooses X, and new voters are added who prefer X over Y, then the set of voters who prefer X over Y have some way of voting to make sure Y does not win without reversing any preferences or falsely voting any candidates equally.)* and the "ultra-strong defensive criterion" (*non-dishonest defensive strategies are always available to larger and/or more-motivated groups (where motivation is counted relative to the Smith set) than the corresponding offensive strategies*). 2009/8/29 Markus Schulze <markus.schu...@alumni.tu-berlin.de> > Hallo, > > it seems to me that Score DSV does not satisfy > monotonicity. It seems to me that the following > scenario is possible: > > Candidate A is the original winner. > > Suppose some voters rank candidate A higher > without changing the order in which they > rank the other candidates relatively to > each other. Then it is possible that some > other candidate B is kicked out of the Smith > set and that, after renormalizing the ballots, > candidate A is worse off. > > Markus Schulze > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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