Arrowian Social Equilibrium: Indecisiveness, Influence and Rational Social Choices under Majority Rule

Abstract

Abstract We introduce the concept of an Arrowian social equilibrium that inverts the schemata of the famous impossibility theorem of Arrow (1950. “A Difficulty in the Concept of Social Welfare.” Journal of Political Economy 58 (4): 328–46) and captures the possibility of aggregating non-rational individual preferences into rational social preferences while respecting the Arrowian desiderata. Specifically, we consider individuals whose preferences may not be complete and who, accordingly, may be indecisive when faced with an issue. Breaking with tradition, we consider the possibility of such individuals drawing on their beliefs about society’s preferences that result from the aggregation process to resolve their indecisiveness. Formally, individual choices are modeled as a rational shortlist method (Manzini and Mariotti 2007. “Sequentially Rationalizable Choice.” The American Economic Review 97 (5): 1824–39), with own preferences followed by society’s as the pair of ordered rationales. This results in a mutual interaction between individual and social choices. We study this interaction using majority rule as the aggregator, with an Arrowian social equilibrium specifying how individual and social choices are co-determined, while requiring the latter to be rational. Our main result identifies minimal levels of societal indecisiveness needed to guarantee the existence of such equilibrium.