Anonymity and Neutrality in Arrow’s Theorem with Restricted Coalition Algebras H. Reiju Mihara † Economics, Kagawa University, Takamatsu, Kagawa 760, Japan March, 1996 [Social Choice and Welfare (1997) 14: 503–512] Abstract In the very general setting of Armstrong (1980) for Arrow’s Theorem, I show two results. First, in an infinite society, Anonymity is inconsistent with Unanimity and Independence if and only if a domain for social welfare func- tions satisfies a modest condition of richness. While Arrow’s axioms can be satisfied, unequal treatment of individuals thus persists. Second, Neutrality is consistent with Unanimity (and Independence). However, there are both dictatorial and nondictatorial social welfare functions satisfying Unanimity and Independence but not Neutrality. In Armstrong’s setting, one can natu- rally view Neutrality as a stronger condition of informational simplicity than Independence. Journal of Economic Literature Classification: D71. Keywords: Arrow impossibility theorem, informational simplicity, coali- tions, Boolean algebras, ultrafilters. The running title is “Anonymity and neutrality in Arrow’s Theorem.” A version of this paper is available as ewp-pe/9411001 from the EconWPA. † The author thanks KamChau Wong, whose comments are used in the proof of Proposition 1. The comments by Andrew McLennan and a referee were helpful. 1