Dynamic bbjective and subjective rationality

Abstract

The objective and subjective rationality model characterizes decision makers (DMs) by two preference relations over uncertain acts and provides a dual perspective on rationality. The Örst preference reáects choices that are rational in an objective sense and the second one expresses choices labeled as subjectively rational. While an objective ranking means that the DM can convince others of the correctness of making them, in a sub jective choice the DM cannot be convinced of the incorrectness of making them. Objective and subjective preferences are represented, respectively, by Bewleyís unanimity rule and a maxmin expected utility, both repre sentations holding the same set of multiple priors. We propose and axiomatize a dynamic model for the objective and subjective rationality theory. The static model speciÖes some set of prior probabilities, which should be then updated in the light of new and rele vant information. We provide two new axioms on the interplay of uncon ditional objective relations and conditional subjective preferences. Such axioms ensure that a conditional subjective relation is also a maxmin ex pected utility preference and the corresponding set of priors is generated by the full Bayesian updating rule. Our main result thus provides a foun dation for sequentially consistent maxmin subjective preferences, where the prior sets are updated according to the prior-by-prior Bayesí rule. Finally, we study the dynamics of objective preferences and its relations with our main result.