Dynamically consistent objective and subjective rationality

A group of experts, for instance climate scientists, is to advise a decision maker about the choice between two policies f and g. Consider the following decision rule. If all experts agree that the expected utility of f is higher than the expected utility of g, the unanimity rule applies, and f is chosen. Otherwise, the precautionary principle is implemented and the policy yielding the highest minimal expected utility is chosen. This decision rule may lead to time inconsistencies when adding an intermediate period of partial resolution of uncertainty. We show how to coherently reassess the initial set of experts' beliefs so that precautionary choices become dynamically consistent: new beliefs should be added until one obtains the smallest "rectangular set" that contains the original one. Our analysis offers a novel behavioral characterization of rectangularity and a prescriptive way to aggregate opinions in order to avoid sure regret.