On Tue, 8 Jun 2004 14:06:19 -0700 (PDT) Forest Simmons wrote:
If I understand correctly, Beat Path, Ranked Pairs, MinMax, and all of the other serious Condorcet methods are in agreement (except for the margins/wv debate) when there are only three candidates: if one of them beats each of the others pairwise, then that candidate is the winner. Otherwise, the cycle is broken at the weakest link.
So why not take advantage of this agreement by using some simple but reasonable method to eliminate all but three candidates and then among those three
If there is a cycle Then break it at the weakest link Else go with the one who beats the other two.
Elimination methods that eliminate all the way down to two candidates offer too much order reversal incentive, but if there is room for three finalists, then that incentive may be negligible.
Here's a more specific proposal along these lines:
Use grade ballots. The three finalists are A the candidate with the greatest number of top grades, B the candidate with the highest grade point average, and C the candidate with greatest number of passing grades.
If all three of these turn out to be the same candidate, then this candidate wins.
If the set {A,B,C} has only two distinct members, then whichever wins pairwise between them is the method winner.
If all three are distinct, and one of them beats the other two pairwise, then that one is the winner.
If there is a three way cycle, then the cycle is broken at the weakest link.
This method is summable, easy to understand, and hard to criticize, though I'm sure the purists will have plenty to say :')
The main disadvantages I see are (1) the controversy over margins versus winning votes, and (2) some folks think that it is too hard to grade the candidates.
Any other proposals for Top Three Condorcet?
Forest
What is a grade ballot?
Anyway, a method using it should not be called Condorcet.
Finally:
If there is no cycle, what is there to brag about here?
If there is a three way cycle, why not solve it via Condorcet?
For other cycles, are we not better off dealing with what should be rarities by agreeing as to how to solve them via ranked ballots?
Note: I still speak only for public elections.
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