Model and Predictive Uncertainty: A Foundation for Smooth Ambiguity Preferences (joint with Tommaso Denti)
Abstract: Smooth ambiguity preferences (Klibanoff, Marinacci, and Mukerji, 2005) describe a decision maker who evaluates each act according to a twofold expectation defined by a utility function, an ambiguity index , and a belief over a set of probabilities. We revisit the logic behind this well known representation. We interpret the set of probabilities as a subjective statistical model, and posit that according to the decision maker it is point identified. Our main result is an axiomatic foundation for this representation within the standard Anscombe-Aumann framework. The result is based on a joint weakening of the Savage and the Anscombe-Aumann axioms. Finally, we extend the analysis to statistical models that are partially identified, in order to capture ambiguity about unknowables.