Bart Ingles said: > > I think there have been several incarnations of Arrow's theorum. The > original 1951 version used monotonicity, IIAC, non-imposition, and > non-dictatorship. I think Alex is describing the 1963 version. Both > are described in the 2nd edition of Arrow's "Social Choice and > Individual Values". It's still in print, I found it on amazon.com.
I found what Bart calls "the 1963 version" in a paper by a a U. Chicago econ prof (http://faculty-web.at.northwestern.edu/economics/chung/mr/Reny.pdf). I'm pretty sure it's also in Saari's book. Also, this link gives the 1963 version: http://www.math.vanderbilt.edu/~bruff/voting/arrow.html In my opinion, Arrow's theorem is more impressive when you have as few assumptions as possible. When the list of incompatible assumptions is large, somebody can say "Well, duh! If you pile on a whole bunch of assumptions you're likely to make the task impossible." But if you have just Pareto, non-dictatorship, and "Independence from Irrelevant Alternative Candidates" (IIAC), it's a more impressive result. Non-dictatorship and Pareto efficiency (if everybody prefers A to B then B never wins) are satisfied by just about any method ever seriously proposed for public elections, so Arrow's Theorem then proves that this single condition (IIAC) is impossible for any seriously proposed method. Alex ---- Election-methods mailing list - see http://electorama.com/em for list info
