A social choice function is said to be implementable if and only if there exists a game form such that for all preference profiles an equilibrium strategy n-tuple exists and any equilibrium strategy n-tuples of the game yield outcomes in the social choice set. A social choice function is defined to be minimally democratic if and only if whenever there exists an alternative which is ranked first by n − 1 voters and is no lower than second for the last voter, then the social choice must be uniquely that alternative. No constraints are placed on the social choice function for other preference profiles. Using the classical definitions of equilibria for n-person games—namely Nash and strong equilibria, it is shown here that over unrestricted preference domains, as long as there are at least as many alternatives as individuals, no minimally democratic social choice function is implementable. A similar result holds in certain restricted domains of the type assumed by economists over public goods spaces. We then show that a different notion of equilibrium—namely that of sophisticated equilibrium—allows for implementation of democratic social choice functions also having further appealing properties.

This paper contains a generalization of the General Possibility Theorem to situations where choice over two-element (more generally, “small”) sets is not possible. The analysis is developed in terms of the social choice function formulation rather than the social welfare function approach. In this formulation, assumptions concerning the size of sets of feasible alternatives are explicit, allowing the role of these assumptions in inducing impossibility results to be explored.

This paper reports experimental tests of three search equilibrium models. These models which differ only in the search strategies available to the buyers have qualitatively different predictions, that is, equilibria: price distributions, single price equilibria at the competitive price and at the monopoly price and two price equilibria. The experimental outcomes generally were consistent with the models' predictions. This suggests that debate on the utility of this class of models should shift to the realism of the models' assumptions rather than focus on their ability to characterize market outcomes. Also, since the basic models have been validated, the project of analysing experimentally the results of relaxing some of their assumptions seems worthwhile.

John A. Ferejohn, David M. Grether, Steven A. Matthews, Edward W. Packel; Continuous-Valued Binary Decision Procedures, The Review of Economic Studies, Vol