EM list-- When I wrote last night, I forgot that there are 2 ways that a voter can change the outcome of a pairwise method. I assumed it would be by reversing the direction of a pair-comparison (which of course would actually require 2 voters, not 1). I forgot that 2 same-voting voters could also change the outcome by changing the outcome of the circular tie solution. That makes for even more of those equally-likely situations that must be considered. So, for each configuration of pairwise defeats, one would consider each way that one could pick a pairwise defeat to be the one that that pair of same-voting voters could reverse the direction of. And also one would consider each way one could pick 2 pairwise defeats to be the ones whose wv is so close that that pair of voters could reverse the magnitude comparison between those two wv numbers. Of course if there are many candidates, and the method drops defeats, and several defeats could be dropped before getting a winner, then you could influence the 1st drop, the 2nd one, or 3rd, etc. *** With any pairwise method, there are situations where different people's strategies can influence eachother's strategy calculations. With Margins & BeatsAll//IRV it's especially difficult to ignore, because something as innocent & ordinary as truncation can work like an offensive strategy. I'd be rather doubful about any strategy calculation for Margins or BeatsAll//IRV that doesn't treat it as a game-theory problem. Maybe the strategy- interaction could be reasonably ignored in Condorcet in the 0-info case, and otherwise too, if we assume no one offensively order-reverses. Mike Ossipoff ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com
