[EM] Hay voting bust, busted

[Peter de Blanc]

On Tue, 2007-02-06 at 19:18 +0100, Jobst Heitzig wrote:
> Dear Peter!
> 
> Sorry to insist, but could you please show that given your new formula 
> it is indeed optimal to vote the true utilities?
> For this you would have to differentiate the expected utility by each 
> expressed rating and show that all these derivatives vanish when the 
> ratings equal the true utilities.
> I have the strong impression that, because of the normalizing constant c 
> which also depends on all expressed ratings, these derivatives are, 
> however, far from being zero,
> meaning that the expected utility is in fact maximized by some set of 
> ratings different from the true utilities!
> 
> Yours, Jobst

Think about the n-Substance problem again. I showed that with a square
root rule, the optimal amount of each substance to buy is proportional
to its utility density. Notice I said "proportional," not "equal." That
proportion is c. So the normalizing constant is not new. All I did was
calculate its value.

You have to have a normalizing constant because the amount of credit you
have available to spend is fixed.