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Many models of economics assume that individuals distort objective probabilities. We propose a simple consistency condition on distortion functions, which we term distortion coherence, that ensures that the function commutes with conditioning on an event. We show that distortion coherence restricts belief distortions to have a particular function form: power-weighted distortions, where distorted beliefs are proportional to the original beliefs raised to a power and weighted by a state-specific value. We generalize our findings to allow for distortions of the probabilities assigned to both states and signals, which nests the functional forms widely used in studying probabilistic biases (e.g., Grether, 1980 and Benjamin, 2019). We show how coherent distorted beliefs are tightly related to several extant models of motivated beliefs: they are the outcome of maximizing anticipated expected utility subject to a generalized Kullback-Liebler cost of distortion. Moreover, in the domain of lottery choice, we link coherent distortions to explanations of non-expected utility like the Allais paradox: individuals who maximize subjective expected utility maximizers conditional on coherent distorted beliefs are equivalent to the weighted utility maximizers studied by Chew [1983].

Barseghyan and Molinari (2023) give sufficient conditions for semi-nonparametric point identification of parameters of interest in a mixture model of decision-making under risk, allowing for unobserved heterogeneity in utility functions and limited consideration. A key assumption in the model is that the heterogeneity of risk preferences is unobservable but context-independent. In this comment, we build on their insights and present identification results in a setting where the risk preferences are allowed to be context-dependent.

We introduce an Attention Overload Model that captures the idea that alternatives compete for the decision maker's attention, and hence the attention that each alternative receives decreases as the choice problem becomes larger. Using this nonparametric restriction on the random attention formation, we show that a fruitful revealed preference theory can be developed and provide testable implications on the observed choice behavior that can be used to (point or partially) identify the decision maker's preference and attention frequency. We then enhance our attention overload model to accommodate heterogeneous preferences. Due to the nonparametric nature of our identifying assumption, we must discipline the amount of heterogeneity in the choice model: we propose the idea of List-based Attention Overload, where alternatives are presented to the decision makers as a list that correlates with both heterogeneous preferences and random attention. We show that preference and attention frequencies are (point or partially) identifiable under nonparametric assumptions on the list and attention formation mechanisms, even when the true underlying list is unknown to the researcher. Building on our identification results, for both preference and attention frequencies, we develop econometric methods for estimation and inference that are valid in settings with a large number of alternatives and choice problems, a distinctive feature of the economic environment we consider. We provide a software package in R implementing our empirical methods, and illustrate them in a simulation study.

We study random joint choice rules, allowing for interdependence of choice across agents. These capture random choice by multiple agents, or a single agent across goods or time periods. Our interest is in separable choice rules, where each agent can be thought of as acting independently of the other. A random joint choice rule satisfies marginality if for every individual choice set, we can determine the individual's choice probabilities over alternatives independently of the other individual's choice set. We offer two characterizations of random joint choice rules satisfying marginality in terms of separable choice rules. While marginality is a necessary condition for separability, we show that it fails to be sufficient. We provide an additional condition on the marginal choice rules which, along with marginality, is sufficient for separability.

We propose and axiomatize the categorical thinking model (CTM) in which the framing of the decision problem affects how agents categorize alternatives, that in turn affects their evaluation of it. Prominent models of salience, status quo bias, loss-aversion, inequality aversion, and present bias all fit under the umbrella of CTM. This suggests categorization is an underlying mechanism of key departures from the neoclassical model of choice. We specialize CTM to provide a behavioral foundation for the salient thinking model of Bordalo et al. (2013) that highlights its strong predictions and distinctions from other models.

In this note, we consider the pricing problem of a profit-maximizing monopolist who faces naive consumers with convex self-control preferences.

This paper illustrates how one can deduce preference from observed choices when attention is not only limited but also random. In contrast to earlier approaches, we introduce a Random Attention Model (RAM) where we abstain from any particular attention formation, and instead consider a large class of nonparametric random attention rules. Our model imposes one intuitive condition, termed Monotonic Attention, which captures the idea that each consideration set competes for the decision-maker's attention. We then develop revealed preference theory within RAM and obtain precise testable implications for observable choice probabilities. Based on these theoretical findings, we propose econometric methods for identification, estimation, and inference of the decision maker's preferences. To illustrate the applicability of our results and their concrete empirical content in specific settings, we also develop revealed preference theory and accompanying econometric methods under additional nonparametric assumptions on the consideration set for binary choice problems. Finally, we provide general purpose software implementation of our estimation and inference results, and showcase their performance using simulations.