> 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. ---- Election-methods mailing list - see http://electorama.com/em for list info