Rational choice by two sequential criteria

This paper contributes to the theory of rational choice under multiple criteria. We perform a preliminary study of the properties of decision made by the sequential application of rational choices. This is then used to obtain a characterization of set-valued choice functions that are rational by two sequential criteria, which follows the approach initiated by Manzini and Mariotti (Amer. Econ. Rev., 2007) for single-valued choice functions. Uniqueness is not guaranteed but our proof is constructive and an explicit solution is provided in terms of approximation choice functions.