Subjective expected lexicographic utility: Axioms and assessment

The theory of subjective expected lexicographic utility brings together two classical developments in expected utility theory. The first is Hausner's theory of expected lexicographic utility in decision under risk. The second is a lottery-based theory of subjective expected utility in decision under uncertainty that was first axiomatized by Anscombe and Aumann. Our synthesis of the two produces representations of preference in decision under uncertainty in which utilities are finite-dimensional real vectors ordered lexicographically and subjective probabilities are real matrices. Axiomatizations of subjective expected lexicographic utility are described for finite and infinite sets of states. Procedures for assessing vector utilities and matrix probabilities are outlined.