Markus Schulze said: > I prefer to say: "The method should be prepared to declare a > winner for everything except for situations where otherwise > Anonymity, Neutrality, Monotonicity, Independence from Clones > or Local Independence from Irrelevant Alternatives is violated."
The situations giving rise to ties can be derived from a symmetry principle (without definitions I don't know whether your criteria amount to the same): If candidate A wins, and all voters then interchange candidates A and B in their rankings, candidate B should win. If candidate C wins, and all voters then interchange candidates A and B in their rankings, candidate C should still win. This principle can help us identify situations in which two candidates must either be tied, or neither candidate wins, irrespective of the method under consideration. Example: 40 A>C>B 40 B>C>A 10 C>A>B 10 C>B>A Suppose that the method selects A in this case. If all voters swap A and B on their ballots we still have the same situation. Our symmetry principle demands that B win, but our original supposition demands that A wins. We hence conclude one of two things. Either 1) C wins (e.g. Condorcet, top 2 voting) or 2) A and B are tied for victory (e.g. IRV, plurality) Alex ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
