[EM] Hay voting bust, busted

[Peter de Blanc]

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