Essential alternatives and set-dependent preferences - an axiomatic approach

In this paper we deal with a broad framework that covers positive and negative aspects of freedom of choice or other factors such as complexity and diversity. In fact, it allows any conceivable interpretation of set dependence. We first provide in this general setting a sufficient condition for the preference of a set A over another set B. This condition generalizes the sufficient condition that appears in Puppe (1996, Proposition 1). We then clarify why our axioms cannot provide a characterization of a unique ordering.