Journal Article On Collective Rationality and a Generalized Impossibility Theorem Get access Peter C. Fishburn Peter C. Fishburn The Pennsylvania State University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 41, Issue 4, October 1974, Pages 445–457, https://doi.org/10.2307/2296696 Published: 01 October 1974

I. Subset choice conditions, 320. — II. Methods for computing C, 323. — III. Two examples, 325. — IV. Discussion, 326.

[Arrow's impossibility theorem can be viewed as requiring that each subset of two social alternatives be a potential feasible subset or environment, with transitive and complete social choices over these subsets for each profile of individual preference orders. The feasibility assumption for every two-alternative subset is relaxed with consequent changes in the social ordering condition. An Arrow-type impossibility result still obtains when the set of social alternatives is the union of two disjoint sets, each of which has two or more elements, and when \{x, y\} is feasible whenever x is from one set and y is from the other. Variants of the basic theorem are included, one of which requires that strict binary social choices be acyclic.]