Another Characterization of Expected Scott-Suppes Utility Representation

Abstract

This paper provides a new characterization of Expected Scott-Suppes Utility Representation (ESSUR). ESSUR combines the Expected Utility Representation with the Scott-Suppes Utility Representation (ESSUR). The latter represents semiorders that formalize preferences with intransitive indifferences. Dalkıran, Dokumacı, and Kara (2018) were the first to provide an axiomatic characterization of ESSUR. Surprisingly, their characterization does not involve any separability axiom, which is essential for numerical representations of preferences on uncountable sets. Candeal and Indurain (2010) were the first to provide a characterization of SSUR on uncountably infinite sets employing a semiorder separability axiom. In this paper, we identify the axioms required on top of those of Candeal and Indurain (2010) in order to obtain a linear Scott-Suppes utility representation, i.e., another characterization of ESSUR.