If preferences are continuous monotone complete preorders, then there is a continuous social choice aggregation rule which respects unanimity and is anonymous. The simple proof of this result involves a straightforward application of well-known properties of the closed convergence topology. I shall demonstrate that there is an easy (in fact, trivial) solution to the social choice problem of finding a continuous aggregation rule which respects unanimity and is anonymous. This is the social choice problem posed by Chichilnisky (1980a) and solved in Chichilnisky (1980b). Then, using algebraic topology and taking the average of C 1 gradients of preferences, Chichilnisky and Heal (1983) show that contractibility of the (domain) space of preferences is a necessary and sufficient condition for the existence of a social aggregation function that is continuous, anonymous, and respects anonymity. The solution presented there is quite complicated mathematically-it requires a manifold structure for a space of preferences. [Chichilnisky (1991) studies the closed convergence topology on preferences in this context; see also the references cited there. However, a major difference is that Chichilnisky (1991) and the literature arising from that paper focuses on the set of strictly convex (continuous or smooth) preference relations, whereas I require only that preferences be monotone continuous complete preorders.]
The purpose of this brief paper is to derive a continuous aggregation rule meeting the same requirements in a rather elementary way which does not involve The research reported here was supported by the National Science Foundation. My results were obtained and an earlier version of this manuscript was written more than ten years ago. Since then, the references were updated and minor expositional alterations (such as substituting first person singular for first person plural pronouns) were made, but the paper is basically unchanged. I am indebted to the editor, two anonymous referees, and especially Michel le Breton for comments regarding final revisions; the usual disclaimer applies. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.