Ambiguity without a state space

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 analyses a third domain of preference: sets of consequential lotteries. Using this domain, we develop a theory of objective ambiguity without explicit reference to any state space. We characterize a representation that integrates a non-linear 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.