Economics Webinar - Lorenz Expect Utility Theory

We characterize all utility functions over risk prospects based on a cardinal utility index. Our main assumption, (Preference-Mixture) Certainty Independence, is the counterpart of certainty-independence in the pure risk setting. We call preferences that have a have a cardinal utility index Lorenz expected utilities (LEUs) and show that they can be represented by a utility function that is the product of expected utility times one minus a general Gini index. We show that this last term quantifies the degree of first-order risk aversion. We then characterize a subset of LEU that we call rank-dependent disappointment averse (RDDA) preferences. These have three parameters: a probability transformation function, λ, a parameter β ≥ 0 and a utility index, u and include rank-dependent expected utility (β = 0) and disappointment aversion (λ is the identity function) as special cases. We characterize risk aversion for RDDA preferences. We provide a definition of Allais-prone behavior and show that an RDDA preference is Allais prone if and only if its λ is a convex power function and either β > 0 or λ is strictly convex. Finally, we show that RDDA preferences are a subset of LEUs called probabilistically sophisticated maxmin expected utility preferences.