On Fri, 14 Mar 2003, [iso-8859-1] Kevin Venzke wrote: > I suspect that this system (applying a Condorcet > method to the ballots) is identical to Borda with a > fixed number of ranks. I'd bet that voters would use > Approval strategy (give only 15's and 0's). > > Given a Borda ballot of A>B>C>D>E, the points given > are A 4, B 3, C 2, D 1, E 0. If you make a Condorcet > matrix reflecting these points, you'll get the same > winner: > A B C D E > A . 1 2 3 4 > B 0 . 1 2 3 > C 0 0 . 1 2 > D 0 0 0 . 1 > E 0 0 0 0 . > > Measuring the degree of preference essentially means > letting this voter vote four times for the A>E > proposition. The value of mere relative ranking is > diluted. I'm not sure this can be overcome.
Your reaction is typical for the first exposure to methods based on dyadic ballots. The main problem with the Borda scoring approach is that it doesn't have fixed boundaries for the relative preference strengths. In the dyadic ballot A>B>>C>D the strength of the AD preference is exactly the same as the strength of the BC preference because the max strength boundary straddled is of the same type for both. In your Borda example of A>B>C>D, the AD preference would be three times as strong as the BC preference. If A were Favorite and B were Compromise, there would be no advantage on the dyadic ballot to rank B over A in the contest between B and C or between B and D. On the Borda ballot B would gain advantage by switching places with A, i.e. by burying Favorite. In the recent method I suggested no entry on any pairwise matrix computed from any ballot is anything other than a zero or a one. Think of it as pairwise matrices constructed from CR ballots of successively greater resolution starting with resolution two (i.e. approval). When it comes to pairwise matrices, the main advantage of using CR ballots over ranked ballots is that equality is allowed at the top and middle as well as the bottom. Now to be more specific about the method. Initialize the order with the pairwise matrix from the resolution two ballots. Locally Kemenize (i.e. bubble sort) with the pairwise matrix from the resolution four ballots. Then locally Kemenize again with the pairwise matrix from the resolution eight ballots. Finally, locally Kemenize again with the pairwise matrix from the full resolution ballots. The method satisfies the Condorcet Criterion as well as any other method (such as MAM) that allows equal rankings and has ballots of resolution limited to sixteen. In any case the winner is a member of the Smith set. The dyadic ballots are merely a way of combining the resolution 2, 4, 8, and 16 ballots into one. Equivalently you could start with an high resolution CR ballot with all ratings represented as binary point expansions between .00000... and .11111... . To get the various low resolution ballots, truncate (rather than round) the ballot ratings to various numbers of binary places. A rating of .1101001011101 could be truncated to .1101 for a resolution 16 ballot, or .1101001 for a resolution 128 ballot, etc. Forest _______________________________________________ Election-methods mailing list [EMAIL PROTECTED] http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com
