Many decisions involve both imprecise probabilities and intractable states of the world. Objective expected utility assumes unambiguous probabilities; subjective expected utility assumes a completely specified state space. This paper analyzes a third domain of preference: sets of consequential lotteries. Using this domain, we develop a theory of Knightian ambiguity without explicitly invoking any state space. We characterize a representation that integrates a monotone transformation of first order expected utility with respect to a second order measure. The concavity of the transformation and the weighting of the measure capture ambiguity aversion. We propose a definition for comparative ambiguity aversion and uniquely characterize absolute ambiguity neutrality. Finally, we discuss applications of the theory: reinsurance, games, and a mean–variance–ambiguity portfolio frontier.

We propose non-parametric definitions of absolute and comparative naivete. These definitions leverage ex ante choice of menu to identify predictions of future behaviour and ex post (random) choices from menus to identify actual behaviour. The main advantage of our definitions is their independence from any assumed functional form for the utility function representing behaviour. An individual is sophisticated if she is indifferent ex ante between retaining the option to choose from a menu ex post or committing to her actual distribution of choices from that menu. She is naive if she prefers the flexibility in the menu, reflecting a mistaken belief that she will act more virtuously than she actually will. We propose two definitions of comparative naivete and explore the restrictions implied by our definitions for several prominent models of time inconsistency.