Numerical Representations for Nontransitive Preferences

Abstract

The authors study the lack of necessity of the transitivity property when representing preference relations. Avoiding transitivity hypothesis, this work offers a vision about the modeling of consumer preference relations which are different from the classic one used in economics pedagogy. The acyclic and the asymmetric nontransitive preference relations, which under certain conditions admit different types of numerical representations, are analyzed. Particularly, the construction of real valued functions which characterize the maximal elements are studied. The authors propose introducing this class of preference relations to intermediate economics students. They justify the acceptation of consumer preference relations without transitivities and they present results ensuring the existence of continuous representations for the preference relation. Proofs and development of examples are carefully made in order to help the student.