Hi, this is James G-A replying to Juho... > >My assumption was that the fact that there are four parties of about >equal size was known. Since I at some point said that these pirates >would be from different countries, maybe also the exact number of >people in each party is known. In most elections that is not known. The >fact that there is a cycle and the direction and strength of it and the >fact that one party is not part of the cycle may or may not be known >(or guessed) in advance.
I'm not talking about knowing it in advance, I'm talking about knowing it after the votes have been cast. Let me clarify, for you seem to have missed my major point. I assume that the pirates have already taken a ranked vote, the result of the vote (the exact numbers that you printed initially (101 A>B>X>C, etc....) are made known to all of them, and then a winner is chosen based on our choice of Condorcet completion method. (This is obviously the most realistic scenario, when you replace "pirate captains" with presidents, etc.) Then, with the pirates knowing how many votes of each kind there were, and knowing how the winner was arrived at by the voting method, the question is how likely is a mutiny under a) minimax(margins) b) a Smith-efficient method. Let's say that a Smith method chose A in this example. You argued that A would be mutiny-prone because there is a large-margin defeat against him. My counter argument is that the pirates can read the election result carefully, and see that yes indeed, a C>A mutiny could succeed, but that it would lead naturally to a B>C mutiny, and possibly later an A>B mutiny, and so on. Hence, the C>A pirates would realize the futility/risk of their potential mutiny, and probably they would not do it. Especially the C>A>X>B voters, who would be especially wary of the second B>C mutiny. This is what you didn't take into account when you formulated your "risk of mutiny" principle, and this oversight is really a fatal to your theory. You assume that voters will look exactly one mutiny ahead, but there is no basis for this assumption. The knowledge of where further mutinies might go should tend to stop an mutiny within the Smith set. However, it will not necessarily prevent a mutiny against a non-Smith candidate, in favor of a Smith candidate, as in my RSTZ example. >I think it is a mathematical fact that if mutiny resistance is accepted >by a country as the target of the election, one must elect the >Condorcet loser in some cases. You can only say that if you totally ignore my argument. >And MinMax (margins) is the correct >voting method if votes are sincere. Why? > >Here our thinking differs. I'm thinking about the probability of the >first mutiny That's just what I'm saying! I'm saying that the first mutiny won't occur if those who would potentially engage in it realize that it leads them into a potentially endless cycle of mutinies, with no guarantee of a more preferable result, and a real chance of a less preferable result. Your failure to take this into account is frustrating. >For Z >the probability of first mutiny is still the smallest. Only based on your arbitrary use of defeat margin as the sole determinant of mutiny probability. As I understand it, mutiny against Z far, far more likely than mutiny against R, S, or T. 100 voters favor R/S/T. 71 voters favor Z. The 100 R/S/T voters realize that they outnumber the Z voters 100-71. They realize that no matter which of the R/S/T candidates ends up ahead, the result will be preferable to Z. I suggest that they will feel that the method has not satisfied majority rule, and I suggest that they will be entirely correct in feeling this. Thus, they will feel justified in taking matters into their own hands. Since they know that they have common cause in a mutiny, they will probably pause to decide which candidate they would like to replace Z with. Once they figure this out, they can happily mutiny. Z will go down, their new captain will go up, and there will be no further mutinies. If R, S, or T is the initial winner, potential mutineers will be soundly discouraged by the possibility of further mutinies, as discussed. >This is a good argument in the pirate world if there are sequential >mutinies, but as I said, I'm mostly focusing on avoiding mutinies >altogether (and consider it a problem of the election if there is even >one). Yes, of course, that's what we're both interested in. This provides further proof that you didn't understand my argument. > >Yes you did to some extent. I however still hide behind the argument >that the risk of first mutiny is the parameter that some election >organizers may want to minimize. " > >Another threatening argument in your example could be the fact that R, >S and T supporters could be seen as one big party. If that was the >case, then they would beat Z clearly 100 against 71. What would my >argument be against this. I think the best explanation in that case is >that people inside the RST party are not able to agree internally which >candidate is best and therefore electing Z from the other party might >be appropriate. Voting methods should minimize the need for outside coordination. ... Sorry to be so harsh. It's just that I spent a lot of time and effort on that e-mail to you, and the fact that you didn't seem to follow the main argument is frustrating to me. my best, James > ---- Election-methods mailing list - see http://electorama.com/em for list info