Dynamic Objective and Subjective Rationality

The objective and subjective rationality model characterizes decision makers (DMs) by two preference relations over uncertainty acts and provides a dual perspective of rationality. The first preference reflects choices that are rational in an objective sense and the second ones express choices labeled subjective rational. While an objective ranking means that the DM can convince others that she is right in making them, in a subjective choice the DM cannot be convinced that she is wrong in making them. Objective and subjective preferences are represented, respectively, by a Bewleyís unanimity rule and a maxmin expected utility, both representations holding the same set of multiple priors. We propose and axiomatize a dynamic Bayesian model for the objective and subjective rationality theory. The static model specifies some set of prior probabilities, which should be then updated in the light of new and relevant information. We provide two new axioms on the interplay of unconditional objective relations and conditional subjective preferences. Such axioms ensure that a conditional subjective relation is also a maxmin expected utility preference and the corresponding set of priors is derived from the full Bayesian updating, i.e., it is generated by the prior-by-prior updating of all unconditional probabilities. Our main result thus provides a novel foundation for sequential consistent maxmin preferences as well as for the full Bayesian updating. Finally, we study the dynamics of objective preferences and its relations with our main result.