Finite and infinite complexity in axioms of rational choice or Sen's characterization of preference-compatibility cannot be improved

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Abstract

Axioms of rational choice are said to have "infinite complexity" if the consistency condition that they posit deals simultaneously not only with pairs, triples, or even arbitrarily large finite collections of decisions, but with infinite collections as well. This short note gives a proof that a characterization of the choice functions which are compatible with an underlying system of pairwise preferences must include an infinite complexity axiom, provided decision sets are not necessarily finite and the underlying preferences not necessarily a complete order.

Original languageEnglish
Pages (from-to)339-346
Number of pages8
JournalJournal of Economic Theory
Volume49
Issue number2
DOIs
StatePublished - Dec 1989

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