CR pairwise

Roy royone at
Wed Aug 29 09:42:35 PDT 2001

Forest Simmons wrote:
> The entry in the i_th row and j_th column M(i,j) is a one or a zero
> depending on whether or not this ballot has a higher rating for
> candidate i than for candidate j .

IMO, this gives too much weight to rankings and not enough to 
ratings. The collapsing strategy uses ratings, but it is only used to
resolve cycles. I don't think that, given the information on a CR
ballot, the Condorcet criterion should apply.

Consider (sincere ratings):

Voters   rate A   rate B   rate C
20       100      50       0
10       50       0        100
70       90       100      0

B is clearly the Condorcet winner, but choosing A brings the rest of 
the voters into the represented group, without badly compromising the 
preferences of the majority. When you know the strength of a 
preference, you can do better than when you only know that a 
preference exists.

If M(i,j) is rating(i)-rating(j), counting only where rating(i) > 
rating(j), I suspect the results will always be the same as the
ordinary way of processing CR. It yields A>B>C for my example.

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