<HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">Let's agree that when we say an Election Method selects the "correct" winner, what we mean by that is that is the winner is consistent with the majority's opinion.<BR>
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When there are only two candidates, this is unambiguous. <BR>
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With three or more candidates it is possible that there are different "majorities", so there are different "election methods" that select one of the majorities to determine the winner.<BR>
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We are all familiar with candidateXcandidate matrix that sums voter's "pairwise" prrefences, but I would suggest that such a matrix is not very useful for determining which of the "majorities" in the pairwise comparisons is the ONE that that is most reflective of the majority of the voters' preferences.<BR>
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Let's forget a moment the pairwise comparisons and instead of looking at things as<BR>
>31: B>A>E>C>D<BR>
>23: C>B>A>E>D<BR>
>25: D>A>C>E>B<BR>
>11: D>C>B>A>E<BR>
>10: E>A>C>B>D<BR>
we examine the ordinal rankings of each candidate by each of the sets of ballots:<BR>
V A B C D E<BR>
31: 2 1 4 5 3<BR>
23: 3 2 1 5 4<BR>
25: 2 5 3 1 4<BR>
11: 4 3 2 1 5<BR>
10: 2 4 3 5 1<BR>
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Now define the Score for a candidate as SUM ( function_of_ordinal_by_voter( candidate ) ). <BR>
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We can describe Plurality by defining function_of_ordinal_by_voter as F(candidate) = 1 for candidates ranked 1 by the voter and F(candidate)=0 for all others. B wins with 31 to 25 to 23 to 11 to 10.<BR>
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Borda is sum over voters with F(candidate) = (number of candidates)-(ordinal_by_voter). A gets: 255, B gets 225, C gets 226, D gets 144, and E 150. By Borda, the plurality winner comes in third and the winner is A even though A got no first place votes.<BR>
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My point is that in discussing the merits of Election Methods, translating the examples into an anlytical form makes it easier to compare results from different methods.<BR>
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It is slightly harder to deal with iterative methods, but it appears to me on the face of it that iterative methods need to be preference-preserving: i.e. if I ranked X and Y on my ballot, when the higher of them is eliminated by an iterative method, the other should get the same weight in the method's vote-counting process as the one that was eliminated. (I.e. when I said X>Y>Z I want my Y>Z to count as much as my X>Y did.)<BR>
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Regards,<BR>
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Paul Kislanko <BR>
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