Characterizations of Smooth Ambiguity Based on Continuous and Discrete Data

In the Anscombe and Aumann (1963) setup, we provide conditions for a collection of observations to be consistent with a well-known class of smooth ambiguity preferences (Klibanoff, Marinacci, and Mukerji, 2005). Each observation is assumed to take the form of an equivalence between an uncertain act and a certain outcome. We provide three results that describe these conditions for datasets of different cardinality. Our findings uncover surprising links between the smooth ambiguity model and classic mathematical results in complex and functional analysis.