On Wed, Apr 14, 2010 at 12:57 PM, Bruce Gilson <[email protected]> wrote: > I tend to think along the following lines. One vote almost never changes a > result. However, if a sufficiently large number of voters change their > behavior together to make a change, the result is what one wants to > consider.
No, that is the point of the Nash equilibrium issue. It might be in the interests of a bloc of "players" to change strategy together, even if one of them is worse off if he changes alone. (Think driving on the left side of the road, if everyone switches to the right side together, then everyone is OK, but not if you switch on your own and everyone stays on the other side. They actually had to do this in various countries, see http://en.wikipedia.org/wiki/Dagen_H ). Most methods will elect a candidate if a majority can coordinate and so, act together to elect that candidate. We need a process that distinguishes between, e.g. plurality and approval voting. With plurality, the top-2 have a massive advantage. A condorcet winner who is not one of the expected top-2, would have a very hard time winning. It is not possible to change the vote in small steps from a non-condorcet winner to a condorcet winner. > I think this may be the same as what Clay means by "moving the result closer." The point is that you have a sequence of voter changes that cause the final change, but each step must be an improvement. With plurality, if you shift your vote from one of the top-2 to the condorcet winner, this represents a decrease in the expected utility. Maybe, we could just define the Nash equilibrium probabilistically. It is a "probabilistic Nash equilibrium", if no change by any voter would increase their expected utility of the result, subject to each voter not being certain how the other voters will vote. Actually, maybe that is the solution in general for Warren's proposal. Rather than defining a Gaussian, each voter's vote is just a probability for each possible legal vote. Effectively, it allows each voter's vote to be a mixed strategy. If A and B are the top-2, then I think the optimal vote under plurality is (nearly) 100% probability to either A or B. If everyone does that, then either A or B will win, with near certainty. Under approval, if A and B are the top-2, but you prefer C, then the optimal strategy is (nearly) 100% AC or BC. If C is the condorcet winner, then C is guaranteed to have an expected utility score of greater than 50% and only one of A and B will have that property. This shifts the top-2 to either A&C or B&C. C thus becomes one of the top-2 and cannot be displaced (by the same standard logic as previously). ---- Election-Methods mailing list - see http://electorama.com/em for list info
