Rob, in my experience typically when there is a Condorcet Cycle there is no Approval Strategy A style equilibrium of the kind you posit in your second message on this topic. However, the method you propose in your earlier message might indeed approach an approval strategy A configuration as a limit without this limit configuration itself being an equilibrium configuration. This is analogous to the fact that a function with a jump discontinuity will approach a different value then the value of the function. * Anyway, I think your first approach is worth exploring further. I'm sure there is something valuable there to be learned. Forest * For example, let f(x) be (x+1)/2 for x<1, and zero otherwise. Then for any starting value x0, the sequence f(x0), f(f(x0)), ... converges to one, but f(1) is zero instead of one. This is analogous to what happens when your Range Strategy A method converges to non-equilibrium Approval Straategy A configuration.
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