Every nonfalsifying method that I know of has, in every situation, an equilibrium that not only doesn't involve order-reversal, but which also elects the sincere CW (The premise of these definitions limits them to situations that have a sincere CW). For that reason, and because an equilibrium that elects the CW is obviously more important & desirable than other equilibria, I'd like to add that to my definition of nonfalsifyingness. Here it all is, with the revisions:
If voters have complete information about eachother's preferences, and if there's a sincere CW, and there's no indifference between that CW and the other candidates (though there could be indifference among those others): A method is falsifying if there's some situation in which it doesn't have any equlibria in which there is no order-reversal and in which the sincere CW wins. A method is doubly falsifying if there's some situation in which it doesn't have any equilibria at all in which there is no order-reversal. A method is nonfalsifying if in every situation it has an equilibrium in which there is no order-reversal and in which the sincere CW wins. A method is strongly nonfalsifying if it is nonfalsifying without the stipulation that there's no indifference between the CW and the other candidates. A method is expressive if in every situation there is an equilibrium in which no one reverses a sincere preference or votes a less-liked candidate equal to a candidate whom that voter has included in his/her ranking, and in which the sincere CW wins. A method is conditionally completely expressive if, in the event that we rule order-reversal out as a strategy, that method has, in every situation, an equilibrium in which everyone sincerely ranks all of the candidates, and in which the sincere CW wins. [end of definitions] Approval is strongly nonfalsifying. Condorcet(wv) is nonfalsifying, expressive, and conditionally completely expressive. Condorcet(margins), IRV, and Plurality are doubly falsifying. (I've verified a few of these statements. I'll verify the rest over the next few days). Mike Ossipoff _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx
