Dear Ken, I wrote (29 Feb 2004): > My favorite formulation of Arrow's Theorem is Pattanaik and Peleg's > formulation (Prasanta K. Pattanaik, Bezalel Peleg, "Distribution of > Power Under Stochastic Social Choice Rules," Econometrica, vol. 54, > p. 909-921, 1986). In their formulation, this theorem says that > there is no rank method that is non-dictatorial and satisfies Pareto > and regularity. "Regularity" says that adding candidate Z should > not increase the probability that candidate A (with A <> Z) is > elected.
You wrote (29 Feb 2004): > But is there any such non-rank method? (I presume "rank" > means a ranked-preference method, which CR is not.) Arrow proved that there is no single-winner election method with the following four properties: 1) It is a rank method (= a ranked-preference method). 2) It satisfies Pareto. 3) It is non-dictatorial. 4) It satisfies IIA. All four properties are needed to get an incompatibility. For example, RandomDictatorship is a paretian rank method that satisfies IIA, RandomCandidate is a non-dictatorial rank method that satisfies IIA, Approval Voting is a paretian non-dictatorial method that satisfies IIA, my beatpath method is a paretian non-dictatorial rank method. ****** You wrote (29 Feb 2004): > So is it correct to say that Arrow did not prove that "there > is no perfect voting system"; he only proved that the methods > he deems to be acceptable are imperfect? Even though the presumption that the used single-winner election method is a rank method is necessary to prove Arrow's Theorem, this presumption is not necessary to prove the Gibbard-Satterthwaite Theorem. The Gibbard-Satterthwaite Theorem says that there is no paretian non-dictatorial method that isn't vulnerable to strategical voting. Markus Schulze ---- Election-methods mailing list - see http://electorama.com/em for list info