I was wondering if anyone -- ha, okay, scratch that, I was wondering *WHO* has looked into using two tie breakers for Condorcet cycles, rather than just one? By that, I mean
1. Find the Condorcet winner 2. If there is a Condorcet cycle, take the Smith (or Schwarz) set 3. Out of this set, find a single winner with method A, and find a single winner with a completely different method B. 4. If both methods pick the same candidate, this person wins, otherwise compare candidates A and B to find the overall winner. Perhaps I should backtrack a bit. I was looking at Yee diagrams today for the umpteenth time (they are a lot of fun). When I was looking at the diagrams for Borda and Plurality, it struck me that if Borda tends to pick centrists, and Plurality tends to pick extremists, it might be interesting to find the winners with each method, and then compare them against each other to choose the overall winner. (As a side note, it would be fun to look at the Yee diagrams of such pairs to see which combined pairs came closest to Voronoi diagrams.) Using the framework above, you'd have: 1. Find the Condorcet winner. 2. If there is a Condorcet cycle, take the Smith set. 3. Find the Plurality winner out of this set. 4. Find the Borda winner out of this set. 5. If both methods pick the same candidate, this person wins, otherwise compare the Borda winner with the Condorcet winner. (In other words, in a three-person tie, you'd drop the candidate that was neither the Borda nor the Plurality winner, and compare the remaining two.) Of course, you could use other methods. I picked Plurality and Borda because they were very simple and acted in opposite ways in certain situations. Plus, it's likely someone has looked into them some time in the past. You might be able to come up with better pairs of methods that have opposing strategies, making strategic voting less useful (or at least more difficult). Michael Rouse ---- Election-Methods mailing list - see http://electorama.com/em for list info
