At 08:59 PM 11/7/2006, David Cary wrote: >Both CRV and Wikipedia claim that range voting meets the Independence >of Irrelevant Alternatives (IIA) criterion, but neither gives much >justification for such claims. > >Electorama succinctly but informally describes IIA as: > "if one option (X) wins the election, and a new alternative (Y) >is added, only X or Y will win the election."
Election criteria are supposed to be objective. One of the aspect of this, and I think it is -- or should be -- standard in applying the criteria, is that the mental state of the voters is not relevant. What is relevant is what is expressed on the ballots. (It was a failure to consider this that resulted in the error of considering Approval to have failed the Majority Criterion.) One can certainly claim that an election method does not allow voters to express something, such as more than two ranks, or preference strengths. But that's not relevant here. What does it mean to "add" a new alternative? In methods that are purely ranked, we presumably assume that the new candidate fits somewhere into the ranking system, and then the votes would be changed accordingly, with no other complications. We would assume that all relative ranks remain the same, for the candidates already in the election, and that the newcomer is simply assigned one of these ranks. If ranks must be exclusive, it is reasonable to allow that a new rank is inserted at some position for the candidate, but, again, except for that additional rank, nothing else changes. The Range equivalent could only mean that the new alternative does not disturb the existing range ratings. And if this is the meaning, Range satisfies IIA, quite clearly. What Mr. Cary did was to assume that the voters were following a strategy where one considers and adjusts Range votes based on the "candidate space." I.e., with this strategy, one ranks the best at max and the worst at zero, and then assigns values in between for the others, based on expectation of value. However, this is internal process, and there are other reasonable strategies for the voter to follow. Moving toward Approval style voting is one of them. Approval satisfies IIA. Only if we think that the voter is following some strategy which causes the voter to change the approval votes already cast based on this newcomer could we say that it does not satisfy it. But this is a ridiculous interpretation of IIA. Or at least it is one that becomes very hard to satisfy. I do not find IIA to be crisply defined. It seems to me that it is a criterion designed for ranked methods, because one may make ready assumptions about the effect of an added candidate on voting, by making presumptions about the effect of rank. The nomination of Genghis Khan would probably not cause me to adjust my Range Votes for any candidate.... I'd simply rank him at zero. The nomination of a candidate that was obviously better to me than anyone else on the list, however, might indeed cause me to change my range ratings, and such adjustments might indeed, if other voters did not agree with me, cause a slippage for one of these such that he loses and the newcomer also loses. But this is hardly an "irrelevant alternative." I'd think of an irrelevant alternative as someone outside the reasonable candidate space, or, alternatively, a clone of a candidate already in that space. These would not ordinarily affect the winner, except possibly to substitute the newcomer for the previous winner, thus satisfying IIA. ---- election-methods mailing list - see http://electorama.com/em for list info
