On Wed, 2007-02-07 at 00:47 +0100, Jobst Heitzig wrote: > Then you should be able to provide a thorough proof that it is optimal > to express rankings proportional to your true utilities, by showing the > respective derivatives to be zero. > > Please do so, since I still question that they are!
Jobst, I can do this for you but it would take me a while to do. I'm not very good at typesetting HTML and the formulae are very ugly and complicated. Let me ask you: in the original writeup for "the n-Substance problem," do you believe that: 0. the pricing rule given satisfies the criterion given (ie that it is optimal to purchase quantities proportional to utility densities)? All I did to get the formulae from Hay Voting from there was: 1. I let the substances be transfers of voting mass between candidates (there are n choose 2 such possible transfers) 2. I calculated exactly how large each transfer would be by assuming that the size of the transfer would be proportional to the difference in utility between candidates. 3. I then calculated how much voting mass each candidate would be left with after all the transfers I thought that each of the steps was adequately justified. If you have a problem with one particular step, then it would be easier for me to try to clarify that. - Peter de Blanc ---- election-methods mailing list - see http://electorama.com/em for list info
