Programs in Preference and Belief Aggregation

Political economy and social choice both have their origins in the Eighteenth Century, in the work of Adam Smith (1759, 1776) during the Scottish Enlightenment and in the work of the Marquis de Condorcet (1785) just before the French Revolution.2 Since then, of course, political economy or economic theory has developed apace. However, it was only in the late 1940's that social choice was rediscovered (Arrow 1951; Black 1948, 1958), and only relatively recently has there been work connecting these two fields. The connection between political economy and social choice theory is the subject matter of this volume. Adam Smith's work leads, of course, to modern economic theory-the analysis of human incentives in the particular context of fixed resources, private goods, and a given technology. By the 1950's, the theorems of Arrow and Debreu (1954) and McKenzie {1959) had formally demonstrated the existence of Pareto optimal competitive equilibria under certain conditions on individual preferences. The maintained assumption of neoclassical economics regarding preference is that it is representable by a utility function and that it is private-regarding or "selfish". The first assumption implies that preference is both complete and fully transitive, in the sense that both strict preference ( P) and indifference (J) are transitive (thus for example if a: and yare indifferent as are y and z, then so are a: and z). The private-regarding assumption means that each individual, i, has a choice space, X;, say, on which i's preferences are defined. In some sense the collective choice space, X, is a subset (with appropriately defined feasibility constraints) of the Cartesian product II; X;. Abstractly, the market is characterized by the existence of an equilibrium mapping E : X X D --+ X. Here D is an appropriate domain of preference profiles (defined perhaps by D = II; D;, where D; is used to characterize the set of permissible preferences fori). A point x within X in the domain of E describes