A space of lexicographic preferences

There are many lexicographic probability systems (LPS’s) that represent the same lexicographic expected utility (LEU) preference relation (Blume et al., 1991). The space of all LPS’s on a Polish space therefore contains redundant representations of preferences. We show that there exists a Polish subspace of LPS’s that represents all LEU preference relations without such redundancies. Our approach is novel in that it frames the question as what is called a Borel section problem in classical descriptive set theory. The results are motivated by conceptual issues relevant to applications in epistemic game theory.