The Common Structure of Paradoxes in Aggregation Theory
Umberto Grandi
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.
Keywords: Computational Social Choice; Judgment Aggregation; Condorcet Paradox