Community preferences and social choice

Abstract

This paper gives necessary and sufficient conditions for the aggregation of preferences, extending an earlier treatment of aggregation by Stolper, Gorman, Samuelson and Chipman. Such aggregation procedures are intended to deal with the problem of aggregating demand functions in econometrics, where the aggregate is required to be independent to the income distribution. Thus, it is usually assumed in this form of aggregation that all consumers face the same prices, but that the distribution of income is unrestricted. In order to establish the characterisation result, we present a new approach to preference aggregation which involves summing certain subsets of the graphs of the preferences, viewed as subsets of a Euclidean space. This procedure has a clear geometrical interpretation, and a number of useful applications. In particular, it enables us to analyse the possibility of aggregation when prices are not constrained to be the same for all consumers, a case of possible empirical significance. We also show that the Stolper-Gorman-Samuelson-Chipman construction of community indifference curves coincides with a special case of this procedure. Finally, this approach allows us to develop the relationship between these forms of aggregation and the preference aggregation problem as it occurs in social choice theory.