# Research

Working Papers:

Euclidean Properties of Bayesian Updating

This paper introduces a simple, automaton-like model to analyze Bayesian updating and non-Bayesian heuristics. The model, called a learning rule, combines a set of belief states with a collection of transition functions over the beliefs. The primary result is an axiomatic characterization of Bayesian learning rules, in which beliefs are distributions over a latent state and transitions follow Bayes’ rule. The second main result characterizes how Bayesian belief-transitions can be represented as vectors in Euclidean space, equipped with geometric notions of magnitude and direction. Applications of the learning rule framework include facilitating belief elicitation from laboratory subjects.

Unacknowledged Heterogeneity in Communication

I analyze a sender-receiver model in which both parties mistakenly believe they share the same interpretation of words, or linguistic convention, when in fact their conventions are drawn independently from a common distribution. Under mild regularity conditions, I find that this form of projection bias leads to systematic distortions of meaning. On average, the receiver exaggerates the sender’s intended message and over-reacts to information even when the parties have aligned interests. I show how the two parties can partially mitigate miscommunication through multiple avenues, including mediation and redundancy, and study extensions to persuasion and social learning.

A Misattribution Theory of Discrimination

This paper analyzes how Fundamental Attribution Error, the tendency to judge others without accounting for their circumstances, warps beliefs about social groups and drives discrimination. I model a self-sustaining cycle in which agents observe outcome (e.g. test score) gaps across groups, mistakenly attribute those gaps to trait (e.g. ability) differences, and then discriminate on the basis of those beliefs, influencing the observed outcome gaps. In equilibrium, agents of different groups agree about the relative ordering of groups by trait level while systematically disagreeing in absolute terms. The paper further characterizes equilibrium beliefs and compares different de-biasing policy alternatives.

Belief Updating with Dissonance Reduction

This paper models a dissonance-reducing learner. The learner suffers utility loss when faced with mutually conflicting information and, in response, distorts how she perceives different pieces of information to increase the apparent agreement among them. Relative to Bayesian updating, the learner always appears partisan. In two-sided debates, she champions one side by exaggerating arguments that support it and downplaying opposing arguments. Her choice of favored side is both influenced by objective evidence and skewed by hotly-debated issues. Her posterior belief is inordinately extreme. Applications to dynamic learning, networks, persuasion, and information-seeking further characterize the learner’s behavior.

Trade-Restricted and Non-Linear Competitive Equilibria

Competitive equilibria need not exist in thin markets with traders whose preferences include complementarities. This paper shows that, when competitive equilibrium fails to exist, efficient and stable trades may alternatively be supported through trade restrictions that confine market participants to a subset of exchange bids. In a trade-restricted competitive equilibrium, markets clear after traders optimally exchange goods subject to linear prices and a specified subset of permitted trades. The paper establishes that trade-restricted equilibria are characterized by several basic properties, including individual rationality and envy-freeness. Moroever, the set of all equilibria permit a natural ordering according to the permissiveness of the trade restriction; equilibria with more permissive restrictions are necessarily more efficient and stable. The set of outcomes supported as trade-restricted equilibria is also shown to be practically equivalent to those supported through anonymous, non-linear pricing. Finally, trade restrictions may facilitate the development of price-based combinatorial exchanges. To demonstrate, this paper develops a modified Tâtonnement algorithm that, in the case of two goods, is guaranteed to converge to a maximally-efficient trade-restricted equilibrium.

Gender Differences in Competition: Evidence from Jeopardy!

With Keith Chauvin and Anna Hopper.

We investigate the impact of gender on strategic decision-making using a dataset of the trivia game show Jeopardy!. In a sample of 3,921 episodes and 232,838 individual trivia clues, women answer clues correctly at a rate 99% that of men but attempt only 84% as many clues. Consequently, women’s average final scores are 79% that of men, and their average cash winnings are 65% that of men. We employ a structural hazard rate model to understand this critical gender gap in clue attempting. In order to attempt a clue, a contestant must be the first to push a signaling button. Our model suggests that although women are generally slower to signal than men, the gender composition of all three contestants is critical. In episodes with a mixed-gender panel, women signal 8% slower than in all-female episodes, and men signal 2% faster than in all-male episodes. Furthermore, while contestants of both genders signal faster in repeat appearances on the show, the speed gain for women is twice that of men. Our results complement prior literature on gender and competition with evidence from a real-world, highly controlled, high-stakes environment that integrates multiple varieties of competitive tasks. Paper available upon request.