  We obtain variants of the classical von Neumann-Morgenstern expected utility
theorem, with and without the completeness axiom, in which the derived
Bernoulli utility functions are Lipschitz. The prize space in these results is
an arbitrary separable metric space, and the utility functions may be
unbounded. The main ingredient of our results is a novel (behavioral) axiom on
the underlying preference relations which is satisfied by virtually all
stochastic orders. The proof of the main representation theorem is built on the
fact that the completion of the Kantorovich-Rubinstein space is the canonical
predual of the Banach space of Lipschitz functions that vanish at a fixed
point. Two applications are given, one to the theory of non-expected utility
theory, and the other to the theory of decision-making under uncertainty.
