Arrovian Social Choice on Economic Domains

Abstract

Since the pioneering work of Arrow (1951, 1963), social choice theory has developed a long tradition of research on the principles that should guide decision-makers when they have to solve conflicts of interests or judgements among the individuals in a group. In the ordinal non-comparability framework considered by Arrow a social choice issue is described by a profile of preferences and a feasible set. A Social Choice Correspondence selects for each social choice issue a subset of outcomes from the feasible set. Arrow focused on three principles. The first one (weak Pareto) puts some constraints on the set of choices for a given preference profile and a given feasible set. The second one (Arrow’s Choice Axiom) demands invariance of the set of choices when the feasible set shrinks in a specific way but the preference profile is fixed. The third one (Independence of Infeasible Alternatives) demands invariance of the set of choices when the preference profile changes in a specific way but the feasible set is fixed. The domain of the social choice correspondence consists of all the pairs of preference profiles and feasible sets that may arise as possible social choice issues. Arrow proved that if the domain contains all possible preference profiles (Unrestricted Preference Domain) and all finite subsets (Unrestricted Feasible Set Domain) then only the dictatorial social choice correspondences meet the three principles. Hereafter the last part of the statement will be referred to as the Arrow inconsistency.