In this paper we study the compatibility of stochastic models of choice with the expected utility treatment of individual risk aversion. We start by showing that the stochastic counterpart of the classical notion of `being more risk averse than' is not feasible if expected utility is used. Furthermore, this negative result is pervasive, it is present everywhere and leads to substantial problems of identification and interpretation of risk parameters in empirical applications. But we also bring positive results. We show that a simple and natural transformation of utilities, the certainty equivalent representation, is free from this problem. Motivated by this positive result, in the last part of the paper we provide axiomatic foundations for the classical stochastic Luce model that uses the certainty equivalent transformation.
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