The Von Neumann/Morgenstern Approach to Ambiguity

38 Pages Posted: 5 Jul 2013

See all articles by Martin Dumav

Martin Dumav

Universidad Carlos III

Maxwell Stinchcombe

University of Texas at Austin

Date Written: May 2013


A choice problem is risky (respectively ambiguous) if the decision maker is choosing between probability distributions (respectively sets of probability distributions) over utility relevant consequences. We provide an axiomatic foundation for and a representation of continuous linear preferences over sets of probabilities on consequences. The representation theory delivers: first and second order dominance for ambiguous problems; a utility interval based dominance relation that distinguishes between sources of uncertainty; a complete theory of updating convex sets of priors; a Bayesian theory of the value of ambiguous information structures; complete separations of attitudes toward risk and ambiguity; and new classes of preferences that allow decreasing relative ambiguity aversion and thereby rationalize recent challenges to many of the extant multiple prior models of ambiguity aversion. We also characterize a property of sets of priors, descriptive completeness, that resolves several open problems and allows multiple prior models to model as large a class of problems as the continuous linear preferences presented here.

Keywords: ambiguity, decision theory, multiple priors, descriptive completeness, continuous linear functionals on spaces of sets, constant and decreasing relative ambiguity aversion, zonoids

Suggested Citation

Dumav, Martin and Stinchcombe, Maxwell, The Von Neumann/Morgenstern Approach to Ambiguity (May 2013). Institute of Mathematical Economics Working Paper No. 480, Available at SSRN: or

Martin Dumav (Contact Author)

Universidad Carlos III ( email )

CL. de Madrid 126
Madrid, Madrid 28903

Maxwell Stinchcombe

University of Texas at Austin ( email )

2317 Speedway
Austin, TX Texas 78712
United States

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