To study intertemporal decisions under risk, we develop a new recursive model of non‐expected‐utility preferences. The main axiom of our analysis is called mixture aversion, as it captures a dislike of probabilistic mixtures of lotteries. Our representation for mixture‐averse preferences can be interpreted as if an individual optimally selects her risk attitude from some feasible set. We describe some useful parametric examples of our representation and provide comparative statics that tightly link decreases in risk aversion to larger sets of feasible risk attitudes. We then present several applications of the model. In an insurance problem, mixture‐averse preferences can produce a marginal willingness to pay for insurance coverage that increases in the level of existing coverage. In investment decisions, our model can generate endogenous heterogeneity in equilibrium stock market participation, even when consumers have identical preferences. Finally, we demonstrate that our model can address the Rabin paradox even in the presence of reasonable levels of background risk.

We study preferences over menus which can be represented as if the agent selects an alternative from a menu and experiences regret if her choice is ex post inferior. Since regret arises from comparisons between the alternative selected and the other available alternatives, our axioms reflect the agent's desire to limit her options. We prove that our representation is essentially unique. We also introduce two measures of comparative regret attitudes and relate them to our representation. Finally, we explore the formal connection between the present work and the literature on temptation.

We study preferences over menus which can be represented as if the agent selects an alternative from a menu and experiences regret if her choice is ex post inferior. Since regret arises from comparisons between the alternative selected and the other available alternatives, our axioms reflect the agent's desire to limit her options. We prove that our representation is essentially unique. We also introduce two measures of comparative regret attitudes and relate them to our representation. Finally, we explore the formal connection between the present work and the literature on temptation.

We study preferences over menus which can be represented as if the individual is uncertain of her tastes, but is able to engage in costly contemplation before selecting an alternative from a menu. Since contemplation is costly, our key axiom, aversion to contingent planning, reflects the individual's preference to learn the menu from which she will be choosing prior to engaging in contemplation about her tastes for the alternatives. Our representation models contemplation strategies as subjective signals over a subjective state space. The subjectivity of the state space and the information structure in our representation makes it difficult to identify them from the preference. To overcome this issue, we show that each signal can be modeled in reduced form as a measure over ex post utility functions without reference to a state space. We show that in this reduced-form representation, the set of measures and their costs are uniquely identified. Finally, we provide a measure of comparative contemplation costs and characterize the special case of our representation where contemplation is costless.

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.