Discussion Paper

7-27-2020

2244

26

#### Abstract

We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the alpha-MEU model of choice under ambiguity (Hurwicz, 1951) can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference \$\succsim^\wedge\$, 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 \$\succsim^*\$, which captures the rankings the DM deems uncontroversial. Under the objectively founded alpha-MEU model, \$\succsim^\wedge\$ has an alpha-MEU representation and \$\succsim^*\$ 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 alpha-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 alpha-MEU model, while we show that, for the baseline model, standard updating rules can be ill-deﬁned.

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