Stochastic Order-Monotone Uncertainty-Averse Preferences

Abstract

In this paper we derive a numerical representation for general complete preferences respecting the following two principles: a) more is better than less, b) averages are better than extremes. To be able to distinguish between risk and ambiguity we work in an Anscombe-Aumann framework. Our main result is a quasi-concave numerical representation for a class of preferences wide enough to accommodate Ellsberg- as well as Allais-type behavior. Instead of assuming the usual monotonicity we suppose that our preferences are monotone with respect to first order stochastic dominance. Preference for averages expresses uncertainty-aversion. We do not make independence assumptions of any form. In general, our preferences intertwine attitudes towards risk and ambiguity. But if one assumes a weak form of Savage's sure thing principle, there is separation between risk and ambiguity attitudes, and the representation decomposes into state-dependent preference functionals over the consequences and a quasi-concave functional aggregating the preferences of the decision maker in different states of the world.

Keywords: Uncertainty-aversion, stochastic orders, Allais paradox, Ellsberg paradox

JEL Classification: D81