A Study of Lexicographic Expected Utility

A relation <^L on a set of real vectors a, b, … is a lexicographic order when a <^Lb if and only if a ≠ b and for every j such that b_j < a_j there is an i < j such that a_i < b_i. A simple and direct derivation is given for a multidimensional utility function whose lexicographically-ordered expected utility vectors preserve an individual's preference order on a set of probability measures. All but one of Hausner's axioms yield an equivalence on the set of preference intervals, and the resulting bet of equivalence classes is shown to account for the hierarchy in the lexicographic structure. A lexicographic utility representation is noted for the finite-dimensional case. When Hausner's other axiom is added, his theorem for lexicographic linear utility is obtained. This theorem is applied to sets of simple and discrete probability measures.