Preferences with grades of indecisiveness

Departing from the traditional approach of modeling indecisiveness based on the weakening of the completeness axiom, we introduce the notion of graded preferences: The agent is characterized by a binary relation over (ordered) pairs of alternatives, which allows her to express her inclination to prefer one alternative over another and her confidence in the relative superiority of the indicated alternative. In the classical Anscombe–Aumann framework, we derive a representation of a graded preference by a measure of the set of beliefs that rank one option better than the other. Our model is a refinement of Bewley's [6] model of Knightian uncertainty: It is based on the same object of representation — the set of beliefs — but provides more information about how the agent compares alternatives.