EM list-- I want to add that my brief description of a simplified voting equilibrium definition was only a sketch, and that there are details that would have to be clarified to make it complete. I wrote it in that form for brevity. The details have been written down. With all the necessary details, it is an exceptionally wordy criterion, but when I use it I'll just sketch it even more briefly than I did here, noting somewhere that the details are available upon request. The UUCC definition seems to me to be complete as written in my letter here. *** Well, in case someone will have an opinion about my attempt at a complete definition of a simpler & more widely-applicable voting equilibrium, why not state the details here. Obviously, with something this wordy, there's plenty of opportunity for errors, omissions, and things unintentionally left vague: *** By a "comparison", I mean the magnitude-order comparison between 2 vote totals. They could be the absolute vote-totals used in point systems such as Plurality, Approval & Borda, or in IRV. Or they could be the scores that determine the winner or the outcome at some step of a circular tie solving method, such as votes-against or margin scores. By "crucial comparison", I mean a comparison whose order, if it were reversed, would change who wins. By "closest crucial comparison", I mean the crucial comparison that is closest to a tie. To vote between a certain candidate-pair means, in a point system, to vote for one but not the other, or to vote so as to give more points to one than to the other. In a rank method it means to rank one of the 2 candidates higher than the other. Of course, the way a voter can affect a comparison in a way favorable to him involves voting between some candidate-pair. For instance, in Plurality or Approval, it involves voting between the 2 expected frontrunners, the candidates whose vote totals are in the closest crucial comparison (the only crucial comparison in this case). In Condorcet, it involves voting to give one candidate a greater votes-against than another, or voting to make one candidate pair-beat another. The voters' strategy decisions are based on the assumption that the strategy is for an individual voter, or for a faction that is so small that the only crucial comparison that it can affect is the one that would be the closest one if that faction didn't vote. That assumption is standard in most strategy discussion. All the voters share the same predictive beliefs, and they all vote to get their most preferred outcome that they can. It's assumed to be nearly certain that a certain comparison will be the closest crucial comparison. By "nearly certain", I mean that it's so certain that each voter feels sure that there's a certain candidate-pair that he should vote between, no matter what other candidate-pair that would prevent him from voting between. But no so certain that he wouldn't improve his expectation some by voting between other candidate-pairs, provided that doing so wouldn't prevent him from voting between that more important candidate pair, the one that would affect the likely closest crucial comparison. How the voter decides which other candidate-pairs to vote between isn't relevant to this definition, or so it seems to me now. In Approval, only improbably inconsistant frontrunner probabilities would make it to a voter's advantage to not vote, additionally, for every candidate that he likes better than the one that he voted for in order to vote between that most important candidate-pair. But it seems to me that this definition doesn't have to talk about how voters determine which other candidate-pairs to vote between. So a simplified & extended voting equilibrium is an outcome, including the officially reported & recorded count results, that is consistant with the belief that a certain comparison is the closest crucial comparison. *** Maybe this isn't of interest, and I don't mean to waste anyone's time, but I post it on the chance that someone might suggest a better approach. But even if no one's interested, I haven't wasted my time, because this is the 1st time that I've typed all this out, to be printed out. *** All I know about compliance is that Approval passes and Plurality, Borda, & IRV fail. *** Mike Ossipoff ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com