Arrovian Impossibilities in Aggregating Preferences over Sets

Given a society confronting a set of alternatives A, we consider the aggregation of individual preferences over the power set A of A into a social preference over A. In case we allow individuals to have any complete and transitive preference over A, Arrow’s impossibility theorem naturally applies. However, the Arrovian impossibility prevails, even when the set of admissible preferences over A is severely restricted by strong axioms that relate preferences over A to preferences over A. In fact, we identify a very narrow domain of lexicographic orderings over A which exhibits the Arrovian impossibility in all of its superdomains. As the lexicographic extension we use is compatible with almost all standard extension axioms, we interpret our results as the strong prevalence of Arrow’s impossibility theorem in aggregating preferences over sets. * Department of Economics, İstanbul Bilgi University