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.

The subjective likelihood of a contingency often depends on the manner in which it is described to the decision maker. To accommodate this dependence, we introduce a model of decision making under uncertainty that takes as primitive a family of preferences indexed by partitions of the state space. Each partition corresponds to a description of the state space. We characterize the following partition-dependent expected utility representation. The decision maker has a nonadditive set function ν over events. Given a partition of the state space, she computes expected utility with respect to her partition-dependent belief, which weights each cell in the partition by ν. Nonadditivity of ν allows the probability of an event to depend on the way in which the state space is described. We propose behavioral definitions for those events that are transparent to the decision maker and those that are completely overlooked, and connect these definitions to conditions on the representation.

Within diversified firms, the negative impact of leverage on investment is significantly greater for high q than for low q segments and significantly greater for non-core than for core segments. This differs substantially from focused firms and is consistent with the view that diversified firms allocate a disproportionate share of their debt service burden to their higher q and non-core segments. We also find that, among low-growth firms, the positive relation between leverage and firm value is significantly weaker in diversified firms than in focused firms. We conclude that the disciplinary benefits of debt are partially offset by the additional managerial discretion in allocating debt service that is provided by the diversified organizational structure.

We study a two-stage model where the agent has preferences over menus as in Dekel, Lipman, and Rustichini (2001) in the first period and then makes random choices from menus as in Gul and Pesendorfer (2006) in the second period. Both preference for flexibility in the first period and strictly random choices in the second period can be, respectively, rationalized by subjective state spaces. Our main result characterizes the representation where the two state spaces align, so the agent correctly anticipates her future choices. The joint representation uniquely identifies probabilities over subjective states and magnitudes of utilities across states. We also characterize when the agent completely overlooks some subjective states that realize at the point of choice.

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.