No-envy, efficiency, and collective rationality

We consider the problem of a fair collective choice function (fair CCF) which maps each profile of extended preference orderings into the set of fair social states (the set consists of alternatives which are both Pareto efficient and envy-free) when such a set exists. Our main objective is to examine compatibility of fair social choices with collective rationality. We formulate desirable properties of collective rationality, and look for CCFs satisfying them. Next, we show that there is no CCF that satisfies most of the choice-consistency properties and a simple concept of fairness simultaneously. Moreover, we reveal that there exists no collective choice function that selects efficient and envy-free states cannot be rationalized by a social preference relation. ∗Department of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo, Japan, 1868601. E-mail: [email protected]; Tel: +81-42-580-8192; Fax: +81-42-580-8195. This paper is part of my Ph. D. Thesis. The author is deeply grateful to Kotaro Suzumura, Koichi Tadenuma, Shinji Yamashige, Kiwako Sakamoto, Peter Lambert, Ryoichi Nagahisa, Yukihiro Nishimura and Toyotaka Sakai, Marc Fleurbaey and two anonymous refrees for helpful comments and also thanks the 21st century Centers of Excellence (COE) project on “Normative Evaluation and Social Choice of Contemporary Economic Systems” for financial support. Any remaining errors are my responsibility.