On Tue, Oct 21, 2008 at 12:06 AM, Kevin Venzke <[EMAIL PROTECTED]> wrote: > I can't understand why you left out the possibility that the "top two" > are considered to be A and C! > > This should be quite possible if A and B are considered more similar to > each other than either is to C.
40 A>B>C 20 B>A>C 40 C>B>A Assume, the strategy is "Best of top 2 plus all better than expected winner". Option 3: expected: C win and A 2nd 40: A+B 20: B+A 40: C That gives A: 60 B: 60 C: 40 Thus this becomes: A+B expected winners Option 4: expected: A win + C 2nd 40:A 20:B+C 40:C+B A: 40 B: 60 C: 60 This becomes: B+C expected winners In both cases, after the poll, the assumptions have to be updated. Option 3 becomes option 1 from my last post. Option 4 becomes option 2 from my last post. Thus the transfers are 1->2 (and B wins) 2->1 (and B wins) 3->1 4->2 Thus no matter which of the 4 are the initial starting assumptions, it ends up in state 1 or state 2. Also, it would only oscillate if the support levels are perfectly balanced. The other possible options should also lead eventually to B wins. Assume that the strategy is " a) Approve the best of top 2 b) Approve all you prefer to the expected winner. Call C the condorcet winner, W the initial expected winner and S the initial second place. Poll number 1: C will get majority approval as he is preferred to W (by rule b) in the strategy) Each voter will approve one or other of the top 2 by rule a. This means that one of them will get less than 50% approval. This means that C is promoted to one of the top 2 after poll number 1. Assume that W is the one who also has majority approval. Poll number 2 C will again get approved by a majority (by both rule a and rule b) W will get less than a majority (as he is the other of the top 2) Nobody else will be approved by a majority (this is a probability). C is now considered the expected winner. Poll number 3 C will again get approved by a majority (by both rule a and rule b) Nobody else will be approved by a majority (by rule b) The effect is that one the condorcet winner becomes the expected winner, he will not be displaced. Also, there is a pretty good chance that he will end up there. Even if "poll 2" doesn't result in C ever winning, the fact that he is always one of the top 2 in polls and his opponent is changing will likely cause the voters to assume that he is the likely winner, and then we move to state/poll 3. Ofc, if there isn't a condorcet winner, then the whole thing goes unstable. ---- Election-Methods mailing list - see http://electorama.com/em for list info
