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An Ordinal Analysis of Risk Aversion

This paper sets out an ordinal theory of choice under risk that is capable of replicating and extending practically all the important results obtained in the EU framework and is yet far more descriptive and no less tractable at the same time. We show in particular that established notions related to risk aversion can be completely characterized by the properties of an ordinal utility function of decision parameters, which can in turn be used to generalize existing results on optimal decisions assuming risk aversion. We further shows that a hypothesis on risk attitudes can account for the full range of putatively paradoxical behavioral patterns including simultaneous gambling and insurance, the reflection effect, and preference reversal and that weaker notions of risk aversion consistent with this hypothesis can be analogously characterized by the properties of the ordinal utility function.