On Mon, 2007-02-05 at 10:47 -0500, Peter de Blanc wrote: > are of how others will vote), because of the small amount of randomness > in the method itself. This means that there should be a one-to-one > correspondence between utility functions and voting strategies.
Sorry, I should have said injective mapping, not one-to-one correspondence. I'll add two more comments: 1. I'm worried that some people might be confused about which substances are being purchased in Hay Voting. The substances are not votes; they're transfers of votes between candidates. If you bought votes, then you would not buy any votes for the candidates that you don't like. But if you're buying transfers, then you would transfer votes from a greater evil to a lesser evil. This is what allows us to discover your preference between the two evils. 2. The more general criterion which Hay Voting satisfies is this: we want a voting method such that, given a probability distribution for how the other voters will vote, the mapping from utility functions to optimal voting strategies is injective. In the original formulation of Hay Voting, this mapping does not depend on the probability distribution. In a deterministic (or "semi-deterministic") method, the mapping would have to depend on this probability distribution. In either case it has to be injective if we want to discover what the voters really want. Hay voting already satisfies this criterion, but we can play around with it to try to make a variant that still satisfies the criterion and also produces a sane outcome for the election (this is what Deterministic Hay Voting was aiming at). ---- election-methods mailing list - see http://electorama.com/em for list info
