Dear Forest! I consider your post, in which you argue in favour of using Random Ballot among the set P of candidates which are not strongly beaten by any other, to be perhaps the most valuable post in the last weeks!
I like that method VERY much: It is quite easily described and motivated, does not require the understanding of any complicated concept like Smith set or defeat strength or cycle or covering, is monotonic, clone-proof, Pareto-efficient, IPDA, gives both the approval winner and the CW a positive probability of winning (at least when they possess some direct support), and introduces just about the right amount of randomness. Here's some further observations I made: When some individuals raise a possible winner, the set P of possible winners can only become smaller and the remaining P-members' probabilities can only increase. When the number n of candidates increases, I conjecture that (i) the expected number of candidates which are more approved than the winner is of the order log(b) asymptotically, and (ii) also the number of possible winners is of the order log(b) asymptotically. In other words, the result is almost approval-optimal and depends only slightly on randomness. (The only doubt I have is that this could be too few randomization since it is still possible that some losing candidate beats all possible winners...) The Condorcet Loser can only win when s/he is the approval winner. Although not independent from 2nd place complaints in Steve's sense, the method fulfils a weaker version of that criterion: When removing a possible winner X, the other possible winners don't turn into losers, and only those losers which were strongly beaten by X can turn into possible winners. A nice example how the method succeeds in finding a comprimise has the following sincere prefs and cutoffs: 51 A>C>>B 49 B>C>>A No Condorcet method will elect the obvious compromise C but instead the CW A. Approval would elect the compromise C but then the A voters would have strong incentive to vote only A in order to elect A. Your method will elect A with 51% probability and C with 49%. What name do you suggest for this excellent method? Yours, Jobst ---- Election-methods mailing list - see http://electorama.com/em for list info