Ted, Russ, Forest, James,Juho and others, I think that Ted's draft public "Definite Majority Choice" proposal is excellent, in the sense that anything that might be slightly better would be more complicated and/or less intuitive.
Two contending methods that use the same style of ballot are James G-A's Approval-Weighted Pairwise and my Approval Margins. I've found a couple of examples that illustrate differences between the three methods. The first is copied from a Sep.22,04 James G-A post. 3 candidates: Kerry, Dean, and Bush. 100 voters. Sincere preferences 19: K>D>>B 5: K>>D>B 4: K>>B>D 18: D>K>>B 5: D>>K>B 1: D>>B>K 25: B>>K>D 23: B>>D>K Kerry is a Condorcet winner. Altered preferences 19: K>D>>B 5: K>>D>B 4: K>>B>D 18: D>K>>B 5: D>>K>B 1: D>>B>K 21: B>>K>D 23: B>>D>K 4: B>D>>K (these are sincerely B>>K>D) There is a cycle now, K>B>D>K On the "sincere preferences" ballots, the approval scores are B48, K46, D43, while on the "altered preferences" ballots, the approval scores are B48, D47, K46. Approval Margins uses a "defeat-dropper" method, measuring the strengths of the defeats by the margins between the approval scores (but like AWP,determines their "directions" purely by the rankings.) Approval Margins: D>K 47-46 (m+1) K>B 46-48 (m-2) B>D 48-47 (m+1) B's defeat, with an approval margin of -2, is the weakest and so is "dropped". B, the Buriers' favourite but the sincere (and voted) Approval winner,wins. DMC gets the same result by eliminating D and K. AWP differs from AM in the way that it weighs defeats. Quoting James: > For a given defeat A over B, the magnitude of the defeat is defined by > the number of voters who place A above their approval cutoff and B below > their approval cutoff. Approval-Weighted Pairwise: D>K 06 K>B 46 B>D 44 AWP elects the sincere CW, K! I used to think that electing the voted approval loser was absurd if we assume that the votes are sincere, but by that logic we should resolve all top cycles by electing the Approval winner. From that point of view, sometimes electing the approval loser is only a degree "worse" than not always electing the approval winner! Still, I don't see this example being a great advertisement for AWP versus AM because the winner is the sincere Approval winner. My next example is the one I used in my last post on AM. An old example given by Adam Tarr. Sincere rankings: 49 R>C>L 12 C>R>L 12 C>L>R 27 L>C>R C is the CW. Suppose there is pre-polling and so the L supporters decide to approve C, while the C supporters sincerely divide their approvals. Further suppose that the R supporters all decide to completely Bury C. Then we might get: 49 R>L>>C 06 C>R>>L 06 C>>R>L 06 C>>L>R 06 C>L>>R 27 L>C>>R Now all the candidates are in the top cycle: L>C>R>L. The approval scores are L82, R55, C51. Approval Margins: L>C 82-51 = +31 C>R 51-55 = -4 R>L 55-82 = -27 AM elects L, backfiring on the Buriers! Unfortunately this time DMC eliminates C, and then the Buriers' candidate R wins. Approval-Weighted Pairwise: L>C 49 C>R 45 R>L 06 AWP gives the same good result as AM! Chris Benham Find local movie times and trailers on Yahoo! Movies. http://au.movies.yahoo.com ---- Election-methods mailing list - see http://electorama.com/em for list info