--- "Robson, Alex" <[EMAIL PROTECTED]> wrote: > A uniform distribution works just as well.
Of course MVT does not require a bell-shaped distribution of political views, but empirically that is what is found in most populations. > There is, of course, a mixed strategy equilibrium. which is what I described. I did not say there would be a Nash equilibrium in pure non-cooperative strategies. The two players nearest the edges move towards the middle player, as I stated. The third player then moves around to get almost half the share. Another player can then jump over to be closest to the edge. The equilibrium for non-cooperative players is indeed a mixed probabilistic strategy. But players who play a cooperative game could agree that since they will over the long run get 1/3 shares, being equal in all characteristics, they may as well settle in one equilibrium. In that case, I don't see why this would not be at the 1/6, 3/6, 5/6 positions. I included the possibility of merging two of the parties into one party. When the Republican Party became a successful 3rd party in 1860, the US quickly reverted to two parties. I don't see why this would not be a pure strategy. If there is no ideological drive, the three parties are better off being two parties. One could then ask why the two parties do not merge into one party. The answer is that in reality, parties operate in more than one dimension. The hot-dog vender analogy works with proportional representation, where each party gets a share of the vote like hot-dog vendors getting a share of the sales, but of course does not apply to winner-take-all plurality voting. With two hot-dog vendors, consumers are best off if the vendors locate at the the 1/4 and 3/4 points, and the vendors are no worse off than if they are both at 1/2. So why could there not be a cooperative outcome where two political parties agree to be at 1/4, 3/4? That would also reduce the threat of minor-parties arising at the edges. That might account for the differences we do see between Republicans and Democrats. In the real world, rivalry does not exclude cooperation. Since empirically there does seem to be a bell-shaped political distribution in the USA, the 1/4 and 3/4 points refer to population, so the difference in ideology would not be large, but not tiny either. Fred Foldvary ===== [EMAIL PROTECTED]
