Stochastically independent randomization and uncertainty aversion

This paper proposes a preference-based condition for stochastic independenc e of a randomizing device in a product state space. This condition is appli ed to investigate some classes of preferences that allow for both independe nt randomization and uncertainty or ambiguity aversion (a la Ellsberg). For example, when imposed on Choquet Expected Utility (CEU) preferences in a S avage framework displaying uncertainty aversion in the spirit of Schmeidler [27], it results in a collapse to Expected Utility (EU). This shows that C EU preferences that are uncertainty averse in the sense of Schmeidler shoul d not be used in settings where independent randomization is to be allowed. In contrast, Maxmin EU with multiple priors preferences continue to allow for a very wide variety of uncertainty averse preferences when stochastic i ndependence is imposed. Additionally, these points are used to reexamine so me recent arguments against preference for randomization with uncertainty a verse preferences. In particular, these arguments are shown to rely on pref erences that do not treat randomization as a stochastically independent eve nt.