On the Necessity of Pairs and Triplets for the Equivalence between Rationality Axioms

This paper is concerned with the axiomatic foundation of the revealed preference theory. Many well-known results in the literature rest upon the ability to choose over budget sets that contain only 2 or 3 elements. This paper shows that for any given choice function, many of the famous consistency requirements, such as those proposed by Arrow, Sen, Samuelson etc., are equivalent if every bundle of goods is chosen from some budget sets, and the domain of the choice function satisfies some set of theoretical properties.