Objective rationality foundations for (dynamic) α-MEU

We show how incorporating Gilboa et al.'s (2010) notion of objective rationality into the α-MEU model of choice under ambiguity can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference ≿^∧, which captures the complete ranking over acts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference ≿^⁎, which captures the rankings the DM deems uncontroversial. Under the objectively founded α-MEU model, ≿^∧ has an α-MEU representation and ≿^⁎ has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline α-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded α-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined.