I was thinking about Arrow's theorem. As I understand it, one statement of the theorem is that you cannot construct a function of individual preference orders that satisfies the conditions IIAC (Independence of Irrelevant Alternative Candidates), Pareto (if all voters prefer A to B then B should not win) and non-dictatorship.
Cardinal Ratings (of which Approval Voting is a special case, and some would argue is a strategically equivalent case) does not, of course, use preference orders as inputs. Hence Arrow's Theorem does not strictly apply to it, as I understand the matter. Let's evaluate CR under the assumption that all voters vote sincerely, i.e. if a voter prefers A to B then he or she assigns to B no more points than she assigns to A. We can also add the assumption that voters always give their first choice the highest rating and their last choice the lowest rating. It certainly satisfies IIAC, if we implement IIAC by saying that voters submit their ballots, and then we tally the results twice, once including candidate C and once disregarding C. The winner should be the same in each case, unless C was the winner the first time. (Of course, if voters knew that C had been removed from the ballot they might adjust strategies. That violates the standard ceteris paribis assumption of economics: All other things being the same.) It satisfies Pareto, if we disregard the case of ties: All voters prefer A to B, and all voters give A and B equal ratings. It obviously satisfies non-dictatorship. Seems to me like we have an election method that satisfies Arrow's criteria, even if the nature of the inputs doesn't satisfy Arrow's Theorem. Am I missing something? Alex ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
