The Common Structure of Paradoxes in Aggregation Theory

Abstract: In this paper we analyse some of the classical paradoxes in Social Choice Theory (namely, the Condorcet paradox, the discursive dilemma, the Ostrogorski paradox and the multiple election paradox) using a general framework for the study of aggregation problems called binary aggregation with integrity constraints. We provide a definition of paradox that is general enough to account for the four cases mentioned, and identify a common structure in the syntactic properties of the rationality assumptions that lie behind such paradoxes. We generalise this observation by providing a full characterisation of the set of rationality assumptions on which the majority rule does not generate a paradox.