A unified treatment of risk and ambiguity within a rank-dependent framework

This paper introduces a rank-dependent decision theory that allows for, explicitly characterizes, and separates probabilistic risk-aversion and ambiguity-aversion. While these phenomena have previously been given independent treatments by theories that extend expected utility in different ways, we provide a unified treatment that preserves the distinctness of each phenomenon. The unified theory holds that a decision-maker assigns ‘as-if’ probabilities to events: where she holds events to be unambiguous, these probabilities are additive, and where she holds events to be ambiguous, they are non-additive and represent her attitude towards ambiguity. The decision-maker then distorts these as-if probabilities according to her attitude towards probabilistic risk, and uses the new weights to assess acts according to rank-dependent utility. We axiomatize this theory and show that assessments of probability, attitudes towards ambiguity, attitudes towards probabilistic risk, and utilities are all distinct features of preference.