Arrow's Choice Research Articles

Independence of irrelevant alternatives and consistency of choice

We show that Arrow's condition of independence of irrelevant alternatives is logically related to conditions of consistency of choice (in particular, to Arrow's choice axiom). The relation, however, is indirect. The link is provided by an independence condition due to Hansson (Synthese, 1969) which applies to fixed agenda social choice rules.

Revealed group preferences on non-convex choice problems

This paper studies the conditions under which the basic results of the revealed preference theory can be established on the domain of choice problems which include non-convex feasible sets; the exercise is closely related to the works of Peters and Wakker (1991) and Bossert (1994). We show that while no continuous choice function can satisfy strong Pareto optimality over the class of all compact and comprehensive choice problems, strong Pareto optimality, Arrow's choice axiom, upper hemicontinuity and a weak compromisation postulate turn out to be necessary and sufficient to represent choice correspondences by continuous, strictly increasing and quasiconcave real-valued functions. Some applications of our main findings to axiomatic bargaining theory are also studied.

Arrovian Social Choice Correspondences

A social choice correspondence is Arrovian if it satisfies Kenneth Arrow's choice axiom and independence of infeasible alternatives. For any such correspondence, there is a large fraction of the population whose preferences are irrelevant to the social decision in a large fraction of situations. The authors consider the case of a finite outcome set, and also an outcome set of positive but finite Lebesgue measure (in some Euclidean space). An unrestricted individual preference domain is assumed. The agenda domain assumption allows for a finite lower bound, possibly greater than two, on the size of a feasible set. Copyright 1996 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Continuous-valued social choice

Let ngt; be any social choice correspondence satisfying a mild continuity condition in addition to independence of unfeasible alternatives (which requires the correspondence to select the same set of alternatives in two situations if the feasible sets are identical in the two situations and, for each individual, the restriction of the preference ordering to the feasible set is the same) and Arrow's choice axiom (which generalizes transitivity). If the society is finite or countably infinite, then ngt; is constant, or dictatorial, or inversely dictatorial, even if the agenda domain is restricted. (The outcome space is normal, connected, and first-countable.).

Nonbinary social choice for economic environments

Assume a finite integer l≥2 and a social choice correspondence Φ mapping each (p, Z) into a nonempty subset Φ (p, Z) of Z, where p is a profile of individual preferences and Z is a set of outcomes of cardinality l or more. Suppose that Φ satisfies Arrow's choice axiom, independence of infeasible alternatives, and the Pareto criterion. If the preference domain is the family of profiles of classical economic preferences over the space of allocations of public goods, then Φ is dictatorial.

Arrow's choice axiom

If a choice correspondence satisfies Arrow's choice axiom then it has a complete and transitive rationalization, even if the domain does not include any sets with fewer than m members, where m is a given positive integer.

Social choice in economic environments

This paper considers the consistency of Arrow's axioms in the choice-theoretic version of his impossibility theorem when natural economic restrictions are placed on individual preferences and on the admissible feasible sets. Both pure public goods and pure private goods environments are considered. It is demonstrated that a social choice correspondence exists that satisfies weak Pareto, independence of infeasible alternatives, nondictatorship, and Arrow's choice axiom on these restricted domains. However, a strengthened version of the independence axiom is shown to result in impossibility theorems.