Hoping for the best while preparing for the worst in the face of uncertainty: a new type of incomplete preferences

Abstract: We propose and axiomatize a new model of incomplete preferences under uncertainty, which we call hope-and-prepare preferences. Act f is considered more desirable than act g when, and only when, both an optimistic evaluation, computed as the welfare level attained in a best-case scenario, and a pessimistic one, computed as the welfare level attained in a worst-case scenario, rank f above g. Our comparison criterion involves multiple priors, as best and worst cases are determined among sets of probability distributions, and is, generically, less conservative than Bewley preferences and twofold multi-prior preferences, the two ambiguity models that are closest to ours.