Hi list, I came up with a criterion for ranked voting systems. I think it is new, though if it isn't I'm sure someone will point that out to me :-)
Criterion: Adding a candidate who is pairwise defeated by the current winner may not cause a different winner to be chosen. Equivalently: If removing a candidate causes a different winner to be chosen, the new winner did not pairwise defeat the removed candidate. Intuitively the criterion feels right... if a new candidate shows up but is immediately defeated by the current winner, it's "nice of you to come, and thank you for playing, but..." This criterion implies Local Independence of Irrelevant Alternatives, and hence Smith, Condorcet, Mutual Majority, etc. It appears stronger than LIIA though: if a new candidate is added who is defeated by the current winner, but itself defeats a candidate who defeats the current winner, then the new candidate is part of the smith set, so LIIA allows for a different outcome, but my criterion demands that the outcome remains the same. It's also attainable: Definite Majority Choice complies with this criterion, as do similar pairwise sorted methods. I haven't checked other methods yet, it would be interesting to see which ones comply, and even more interesting to see a concrete case that complies with LIIA but violates my criterion... Also, can anyone think of a good name for it? I think "Strong Local Independence of Irrelevant Alternatives" is getting a bit verbose ;-) - xmath -- Matthijs van Duin -- May the Forth be with you! ---- election-methods mailing list - see http://electorama.com/em for list info
