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.