Informational Requirements for Social Choice in Economic Environments∗

Arrow’s celebrated theorem shows that the aggregation of individuals’ preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individuals’ preferences over that pair, unless the fundamental Pareto and non-dictatorship principles are violated. In a unified approach covering the theory of social choice and the theory of fair allocation, we investigate how much information is needed to rank a pair of allocations by social ordering functions and by allocation rules satisfying the Pareto principle and anonymity. In the standard model of division of commodities, we show that knowledge of a good portion of indifference hypersurfaces is needed for social ordering functions, whereas allocation rules require only knowledge of marginal rates of substitution. JEL Classification Numbers: D63, D71. ∗The authors thank A. Leroux for a stimulating discussion, A. Trannoy for comments, and participants at seminars at the University of Cergy-Pontoise, the University of Rochester, and the 5th International Meeting of the Society of Social Choice and Welfare in Alicante. Financial support from the Ministry of Education of Japan (the Scientific Research Grant No. 10045010 “Economic Institutions and Social Norms: Evolution and Transformation”) is gratefully acknowledged. †CATT, THEMA, IDEP, University of Pau, Av. du Doyen Poplawski, 64000 PAU (France). Email: [email protected] ‡Institute of Economic Research, Hitotsubashi University, Kunitachi, Tokyo 186-8603 (Japan). Email: [email protected] §Graduate School of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601 (Japan). Email: [email protected]