  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.
