On Mon, 2005-11-21 at 16:00 -0600, Paul Kislanko wrote: > I have a personal distrust of methods that "score" by looking at only the > contents of the pairwise matrix, but there should surely be a mapping from > the CW back to the ballots that contributed to the CW being the CW. Take > those ballots and remove all winners, moving up all alternatives ranked > lower than the winner. Then form a new pairwise matrix from the revised > ballots, etc.
Suppose there are candidates A, B, C and D. B is the Condorcet winner and has the following pairwise results: 45-5 B:A 37-13 B:C 29-21 B:D Now, the B v. D result is the pivotal result as it is the closest result of the three. Therefore, it is the most critical one in contributing B to be the Condorcet Winner (I hope I got the gist of your post correct here). So, let's convert the results to margins: +40 B:A +24 B:C +8 B:D Now, it could be argued that we are heading towards a MinMax(Margins) type method here. And MinMax methods look directly at the pairwise matrix. Carrying this further, we then need to remove the ballots that contributed to B being the Condorcet Winner. That is, of the ballots that ranked B>D, 8 need to be removed (or 9, depending on your point of view). But which 8 (or 9)? That is at best non-trivial. Thinking more about the "mapping" idea, the pairwise matrix is really only a way of "mapping" ballots into a convenient form so as to determine an election result. I don't think somebody throwing a load of ballots at me and them asking me to give a result "just like that" is reasonable. That is unless the person doesn't mind me using the Random Ballot method. The only alternative "mappings" I can think of are methods that are Condorcet compliant. Is Borda a Condorcet compliant method? From my vague recollections, I think there are other methods that are Condorcet compliant but don't use a pairwise matrix. Thanks, Gervase. ---- election-methods mailing list - see http://electorama.com/em for list info
