Bayes' rule has two well-known limitations: 1) it does not model the reaction to zero-probability events; 2) a sizable empirical evidence documents systematic violations of it. We characterize axiomatically an alternative updating rule, the Hypothesis Testing model. According to it, the agent follows Bayes' rule if she receives information to which she assigned a probability above a threshold. Otherwise, she looks at a prior over priors, updates it using Bayes' rule for second-order priors, and chooses the prior to which the updated prior over priors assigns the highest likelihood. We also present an application to equilibrium refinement in game theory.

This paper studies, theoretically and empirically, the role of overconfidence in political behavior. Our model of overconfidence in beliefs predicts that overconfidence leads to ideological extremeness, increased voter turnout, and stronger partisan identification. The model also makes nuanced predictions about the patterns of ideology in society. These predictions are tested using unique data that measure the overconfidence and standard political characteristics of a nationwide sample of over 3,000 adults. Our numerous predictions find strong support in these data. In particular, we document that overconfidence is a substantively and statistically important predictor of ideological extremeness, voter turnout, and partisan identification.

We introduce Cautious Utility, a new model based on the idea that individuals are unsure of trade‐offs between goods and apply caution. The model yields an endowment effect, even when gains and losses are treated symmetrically. Moreover, it implies either loss aversion or loss neutrality for risk, but in a way unrelated to the endowment effect, and it captures the certainty effect, providing a novel unified explanation of all three phenomena. Cautious Utility can help organize empirical evidence, including some that directly contradicts leading alternatives.

Many violations of the Independence axiom of Expected Utility can be traced to subjects' attraction to risk-free prospects.Negative Certainty Independence, the key axiom in this paper, formalizes this tendency.Our main result is a utility representation of all preferences over monetary lotteries that satisfy Negative Certainty Independence together with basic rationality postulates.Such preferences can be represented as if the agent were unsure of how risk averse to be when evaluating a lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one.The set of utilities is unique in a well-defined sense.We show that our representation can also be derived from a 'cautious' completion of an incomplete preference relation.

A growing literature has shown that people sometimes prefer to randomize between two options. We investigate how prevalent this behavior is in an experiment using a novel and simple method. Subjects face a list of questions in which one of the alternatives is fixed and the other varies, like a Multiple Price List, but in each row they can randomize between the options. We find that the majority of subjects chose to randomize in the majority of questions, and notably, they did so for ranges of values that were “very large.”

We conduct an experiment in which subjects face the same questions repeated multiple times, with repetitions of two types: (1) following the literature, the repetitions are distant from each other; (2) in a novel treatment, the repetitions are in a row, and subjects are told that the questions will be repeated. We find that a large majority of subjects exhibit stochastic choice in both cases. We discuss the implications for models of stochastic choice.

We study stochastic choice as the outcome of deliberate randomization. We derive a general representation of a stochastic choice function where stochasticity allows the agent to achieve from any set the maximal element according to her underlying preferences over lotteries. We show that in this model stochasticity in choice captures complementarity between elements in the set, and thus necessarily implies violations of Regularity/Monotonicity, one of the most common properties of stochastic choice. This feature separates our approach from other models, e.g., Random Utility.

We investigate the classical Anscombe–Aumann model of decision-making under uncertainty without the completeness axiom. We distinguish between the dual traits of “indecisiveness in beliefs” and “indecisiveness in tastes.” The former is captured by the Knightian uncertainty model, the latter by the single-prior expected multi-utility model. We characterize axiomatically the latter model. Then we show that, under independence and continuity, these two models can be jointly characterized by means of a partial completeness property.

We study preferences over lotteries in which both the prize and the payment date are uncertain. In particular, a time lottery is one in which the prize is fixed but the date is random. With Expected Discounted Utility, individuals must be risk seeking over time lotteries (RSTL). In an incentivized experiment, however, we find that almost all subjects violate this property. Our main contributions are theoretical. We first show that within a very broad class of models, which includes many forms of nonexpected utility and time discounting, it is impossible to accommodate even a single violation of RSTL without also violating a property we termed Stochastic Impatience, a risky counterpart of standard Impatience. We then present two positive results. If one wishes to maintain Stochastic Impatience, violations of RSTL can be accommodated by keeping Independence within periods while relaxing it across periods. If, instead, one is willing to forego Stochastic Impatience, violations of RSTL can be accommodated with a simple generalization of Expected Discounted Utility, obtained by imposing only the behavioral postulates of Discounted Utility and Expected Utility.

This paper develops axiomatically a revealed preference theory of reference-dependent choice behavior. Instead of taking the reference for an agent as exogenously given in the description of a choice problem, we suitably relax the Weak Axiom of Revealed Preference to obtain, endogenously, the existence of reference alternatives as well as the structure of choice behavior conditional on those alternatives. We show how this model captures some well-known choice patterns such as the attraction effect.