[EM] Hay voting bust, busted

[Jobst Heitzig]

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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