Dear Warren! I may be a little late in this discussion but I think you were right when stating something was wrong:
Either way, the expected utility is Eu = sum_k ( u_k * p_k ) where the probabilities p_k sum up to 1. The Hay Voting mechanism converts a set of expressed ratings into a set of probabilities p_k, in a way I don't exactly understand in detail, but it cannot change the fact that the p_k will have to sum up to 1 in the end! Formally, it seems that the question is whether there is a vector of functions p_1,...,p_n of a vector r_1,...,r_n of ratings such that p_1+...+p_n = 1 and such that Eu is at least at a local maximum for r_i := u_i. Can anyone tell me what exactly the probabilities are supposed to be in the original Hay Voting suggestion, or at least what other choice of functions p_i would fulfil the above requirement? Because I was not able to find such functions withing several hours... At least I guess they will rather contain logs than square roots! This is certainly an interesting math exercise, it seems. Yours, Jobst Am Montag, 5. Februar 2007 09:07 schrieb Warren Smith: > Sorry, I appear to have been an idiot. Peter de Blanc > answered my complaints at > http://www.spaceandgames.com/?p=8 > > and it looks to me like I NOW have to agree with Forest Simmons that > this IS a great new contribution to voting theory. > Also, I showed there in my comment how to generalize their scheme > by adding a parameter P. It looks liek the best P is P=0.99 or > so, not P=0.5 (their value) or P=0+ (my value from before). > > Warren D Smith > http://rangevoting.org > ---- > election-methods mailing list - see http://electorama.com/em for list > info
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