[EM] Re: Condorcet, Weber and Info

[Gervase Lam]

> From: Gervase Lam
> Date: Sun, 7 Mar 2004 13:59:27 +0000
> Subject: [EM] Condorcet, Weber and Info

> All that
> needs to be known is whether you think one candidate is better than
> another.  However, I get the feeling that Utilities will matter more the
> more complicated the scenario.

The last sentence is "wrong".  Using Weber's formula and methodolgy always 
results in a ballot matrix that is exactly the same as the voter's sincere 
ranking.

This is caused by the Ui - Uj term in the Weber formula Pi * Pj * (Ui - 
Uj).  If the voter sincerely would rank candidate I higher than candidate 
J, then the difference is positive.  If the voter sincerely would rank 
candidate I lower than candidate J, then the difference is negative.  This 
produces a "Weber matrix" that is a mixture of positive and negative 
numbers.

As a result, the most suitable ballot matrix will always zero out the 
negative numbers.  The positive numbers will always be kept.  A positive 
number means that candidate I has been sincerely ranked above candidate J. 
 Therefore, the ballot matrix will always equal the voter's sincere 
ranking.

Thanks,
Gervase.