On Wed, Jan 9, 2013 at 6:48 PM, Jameson Quinn <[email protected]> wrote:
>> I suggest that you'll find that no non-probabilistic and >> non-dictatorial method can meet Strong IIAC, as defined above. > I agree. However, they will break it with different probabilities, given a > universe of scenarios. For a realistic universe, I suggest MJ will break it > less often than Approval or Score. But the critrerion's premise stipulates optimal voting. Voting to maximize one's utilitly-expectation. That's extreme voting. That's voting as in Approval. Score's optimal strategy is known too: extreme voting. Optimal voing is a fair stipulation for a Strong IIAC. You said that MJ's 0-info optimal strategy is utility-proportional rating. We certainly don't have 0-info elections, as I said earlier. In fact, we have non-0-info u/a elections, in which the optimal strategies of MJ, Approval and Score are to top-rate the acceptables and bottom rate the unacceptables. > I realize that the above claim is unsubstantiated. But note that I above > agree with an unsubstantiated claim. For this purpose, it isn't necessary to prove that all non-probabilistic, non-dictatorial methods fail Strong IIAC. It's enough to say (and demonstrate it if necessary) that MJ fails it. Suppose that some set of voters prefer X to Y, and Y to Z. But their utility difference for X vs Y is very, very small in comparison to their utility difference for X & Y vs Z. Their optimal strategy in MJ is to top-rate X and Y, and bottom rate Z. Now Z withdraws. Now there are only two candidates. Those voters' optmal strategy is now to top-rate X and bottom rate Y. If that set of voters is large enough, that could change the winner from Y to X. Why would MJ fail Strong IIAC less often than would Approval and Score? In particular, in our non-0-info u/a elections? > 2013/1/9 Michael Ossipoff <[email protected]> >> >> Strong IIAC: >> ----------------- >> >> Premise: >> >> An election is held. Everyone votes so as to maximize their utility >> expectation, based on their utility-valuations of the candidates, and >> their estimates or perceptions of any relevant probabilities regarding >> how people will vote, or of count-occurrences such as particular >> pair-ties. >> >> After the election is counted, and the winner recorded, but before any >> results are announced to anyone other than the counters, one of the >> candidates, who isn't the winner, is hit and killed by a car. Because >> a different candidate-set could cause people to vote differently, a >> new election is held. >> >> Again, people vote so as to maximize their expectation, as described >> in the first paragraph. >> >> Requirement; >> >> The winner of the 2nd election must be the same as the winner of the >> 1st election. >> >> [end of Strong IIAC definition] >> >> ---------------------------------------------------------------------- >> >> If it sounds as if it would be difficult to determine whether a method >> meets that criterion, then I remind you that the example-writer is >> free to devise _any_ example that complies with the criterion's >> premise. The example-writer can choose a simple but extreme example >> with particularly extreme or simplified utilities and probability >> perceptions. >> > ---- Election-Methods mailing list - see http://electorama.com/em for list info
