Objective and subjective rationality and decisions with the best and worst case in mind

We study decision under uncertainty in an Anscombe–Aumann framework. Two binary relations characterize a decision-maker: one (in general) incomplete relation, reflecting her objective rationality, and a second complete relation, reflecting her subjective rationality. We require the latter to be an extension of the former. Our key axiom is a dominance condition. Our main theorem provides a representation of the two relations. The objectively rational relation has a Bewley-style multiple prior representation. Using this set of priors, we fully characterize the subjectively rational relation in terms of the most optimistic and most pessimistic expected utilities.