Foundations of ambiguity models under symmetry: alpha-MEU and smooth ambiguity

The alpha-MEU model and the smooth ambiguity model are two popular models in decision making under ambiguity. However, the axiomatic foundations of these two models are not completely understood. We provide axiomatic foundations of these models in a symmetric setting with a product state space, S^{\infty}. This setting allows marginals over S to be linked behaviorally with (limiting frequency) events. Bets on such events are shown to reveal the i.i.d. measures that are relevant for the decision maker's preferences and appear in the representations. By characterizing both models within a common framework, it becomes possible to better compare and relate them.