Stochastic Independence and Uncertainty Aversion

Abstract

This paper proposes a preference-based condition for stochastic independence of a randomizing device in a product state space. This condition, when imposed on Choquet Expected Utility preferences in a Savage framework displaying uncertainty aversion, results in a collapse to Expected Utility (EU). In contrast, Maxmin EU with multiple priors preferences continue to allow for a very wide variety of uncertainty averse preferences when stochastic independence is imposed. These points are used to reexamine recent arguments against preference for randomization with uncertainty averse preferences. In particular, these arguments are shown to rely on preferences that do not treat randomization as a stochastically independent event.

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