Saharon Shelah is one of the best logicians in the world. Which normally means nobody pays attention to him and his work is very hard to penetrate. There's nothing like modern mathematical logic for really driving you straight to the nuthouse.
But it seems Shelah wrote a 46 page (!!) paper on Arrow's theorem in voting: http://arxiv.org/abs/math/0112213 Not easy to read. Apparently the point is this. Arrow's original theorem considered rank-orderings as votes and also as the output of the voting method. Shelah calls these "rational." What if we allow "irrational" votes? "Irrational" means on every subset of the candidates, there is a "best" candidate. Normally that would simply be the first element of the subset ("first" according to some ordering). However, Shelah abnormally says each subset could have some best (or otherwise distinguished) element without any overall ordering enforcing logical consistency... Even in a very general framework of that ilk, Shelah still is able to prove an "impossibility theorem"... but so far I have not been able to translate it into anything I feel I comprehend. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) ---- Election-Methods mailing list - see http://electorama.com/em for list info
