A lot's been written about voting theory, and I know none of it beyond a quick google search, as suggested above. That didn't uncover what occurred to me, although the #Rated_voting_methods may in fact subsume it. But I couldn't quite see how to demonstrate that one way or the other.
It's the slimey (what else?) candidate field in the current nyc mayoral race that suggested this to me. Maybe you don't care so much who (among the slime) wins, but there's one particularly slimey candidate whom you really want to see lose.
So give each voter a choice: you can either mark your ballot "pro" for the candidate you want to win, or "anti" for the one you want to lose. If you vote pro then that guy gets +1 votes, or if you vote anti then -1 votes. The guy with the highest (or least negative if all voters hate every candidate) score wins. An alternative voting scheme might allow each voter to mark their ballot with both one pro and one anti vote.
For n=2 candidates there's obviously no difference; an anti vote for one is equivalent to a pro vote for the other. But for n>2 this scheme is clearly different than the usual one: an anti vote accomplishes something different vis-a-vis the election outcome than a pro vote. But I can't quite figure out how to characterize that difference mathematically. And that #Mathematical_criteria discussion didn't seem quite rigorous enough to do it, either.
So (a) how would you formulate this scheme (or any scheme, for that matter) and the usual scheme is such a way that they can be compared? And (b) is the above scheme equivalent to, or subsumed by, the #Rated_voting_methods scheme (and please prove your answer, if possible)? -- John Forkosh ( mailto: email@example.com where j=john and f=forkosh )