Revealed preference and the axiomatic foundations of intransitive indifference: The case of asymmetric subrelations

Abstract

This paper provides an axiomatic structure for various binary preference relations that are reflexive, connected, and transitive in their asymmetric subrelations known as quasi-transitive orderings. A choice function generates various (distinct) binary preference relations, such as the base relation, the revealed preference relation, and the wide revealed preference relation. For each interpretation of a binary preference relation, we present an axiom that ensures the existence of a quasi-transitive preference ordering. A description of a choice procedure is considered which one often observes in real life and it is shown that the path independence of such a procedure is a sufficient condition for a quasi-transitive ordering of various binary preference relations.