Expected multi-utility representations

This paper axiomatizes expected multi-utility representations of incomplete preferences under risk and under uncertainty. The von Neumann–Morgenstern expected utility model with incomplete preferences is revisited using a ‘‘constructive’’ approach, as opposed to earlier treatments that use convex analysis. © 2012 Elsevier B.V. All rights reserved. ‘‘Of all the axioms of utility theory, the completeness axiom is perhaps the most questionable. Like others of the axioms, it is inaccurate as a description of real life; but unlike them, we find it hard to accept even from the normative viewpoint.’’ (Aumann [1962], p. 446)