Strategy-Proofness and Social Choice Functions without Singlevaluedness - Kelly, Jerry S. (Econometrica, 1977)
FOLLOWING ON SOME informal conjectures by Dummett and Farquharson [3] and Vickery [20] we now have independent proofs by Gibbard [7] and Satterthwaite [17 and 18] that no collective choice rule exists whose social choice functions are singlevalued, strategy-proof, nondictatorial and have a range containing at least three alternatives. Because strategy-proof ness seems desirable and because it is closely related to mainstream economic theory issues of evaluating resource allocation institutions with respect to incentive compatibility (cf. Hurwicz [9]), their theorem has excited considerable attention [5, 6, 10, 11, 12, 13, 14, 15, 16, 19, and 21]. In this paper, the requirement of singlevaluedness is dropped and explorations are made of the consequences this has on the Gibbard-Satterthwaite results. Let E be the set of all alternatives (which must, by assumption, be mutually incompatible) and N= {1, 2,.. ., n} be the set of individuals. A nonempty subset, v, of E (i.e., an element of 2E _-0\