Job Market Paper
Successful communication with natural language requires a sender and receiver to share the same understanding of the meaning of words, or linguistic convention. What happens when people think they share the same convention, but in fact they do not? This paper shows how unacknowledged heterogeneity leads to systematic bias. I analyze a sender-receiver model in which both parties' conventions are drawn independently from a population satisfying a basic regularity condition. Relative to linguistic anchor states that all conventions express identically – such as minimum, maximum, or midpoint states – the receiver on average exaggerates the sender’s intended message. The model therefore predicts over-reaction to information across a range of communication settings, such as economic forecasting, risk calibration, and doctor-patient relations. This occurs even when the parties have completely aligned interests. A sender and receiver with aligned interests can mitigate miscommunication by rephrasing the form of the message sent, garbling the sender’s information, introducing a mediator, or including a redundant second sender. When the two parties have conflicting interests, the receiver always suffers from unacknowledged heterogeneity, but a sender seeking to warp the receiver’s action can benefit from the exaggeration effect. When multiple, similarly biased, agents aggregate information by communicating in sequence, all agents will mistakenly perceive the sequence converging to a point belief, when in fact the limiting distribution is noisily centered on an exaggeration of the true state.
Revise and Resubmit, American Economic Journal: Microeconomics
Individuals often make inferences about others without considering the circumstances that other people face. I analyze the consequences of this psychological bias in a model of discrimination. Each group in a population has an observable distribution of outcomes that is produced jointly by the private traits of group members and the beliefs which all population members have about that group. However, biased observers ignore the role of others' beliefs in generating outcomes, instead drawing inferences about groups under the assumption that traits lead directly to outcomes. There is a unique equilibrium in which beliefs about different groups generate outcomes that are misinterpreted as the original beliefs. In equilibrium, each group's true mean trait is exaggerated relative to a population-wide average; at least one group is overestimated, and at least one group is underestimated. The ordering of groups by outcome levels matches the ordering under correct beliefs for low levels of bias but is arbitrary for sufficiently high levels of bias. Observers of different groups agree in their beliefs about the ordering of groups but systematically disagree in their absolute beliefs. Large levels of bias are shown to unambiguously diminish social welfare. De-biasing policies which lead to corrective preferential treatment for underestimated groups have a multiplier effect in correcting beliefs. By contrast, policies which broaden the diversity of social networks can only correct beliefs about a strict subset of groups.
This paper introduces a novel framework for analyzing Bayesian updating and non-Bayesian heuristics. A learning rule consists of an arbitrary set of belief states and a set of transition functions, called arguments, from the belief set to itself. Bayesian learning rules, with beliefs in the form of probability distributions over a state and arguments in the form of Bayes' rule, are a special case. The paper's first main result is an axiomatic characterization of Virtual Bayesian learning rules, which can be turned into a Bayesian via a relabeling of the set of beliefs. There are three substantive axioms – that arguments are injective functions, that arguments commute, and that repeated application of an argument never produces cycles of beliefs – as well as three regularity assumptions. The axioms both identify the algebraic properties common to all Bayesians and distinguish which among familiar updating heuristics are Virtual Bayesians. The second main result establishes that any Virtual Bayesian learning rule can be embedded into Euclidean space – and therefore equipped with geometric notions of magnitude, direction, etc. – by defining the ‘agreement' between pairs of arguments in a suitably additive manner. Applying such an embedding, an argument's direction corresponds to the limit of the support of posterior beliefs under repeated application of the argument, and its magnitude is the extent to which a single application pushes prior beliefs towards that limit. The paper discusses how the framework of learning rules could be applied to additional contexts, including the elicitation of beliefs from laboratory subjects.
This paper introduces a formal model of a dissonance-reducing learner who suffers utility loss when faced with mutually conflicting information and, in response, selectively distorts her perception of different pieces of information to increase the perceived agreement among them. Relative to a Bayesian updater, the learner exhibits a particular form of partisanship. In a two-sided debate, she favors one side over the other by exaggerating all arguments that support her favored side and mitigating all opposing arguments. The distortion leads her to an unduly extreme posterior belief. Nonetheless, her favored side coincides with the objective balance of evidence. In a dynamic setting, the learner is subject to conversions, in which she switches from being one side’s partisan to identifying with the other side; ultimately the agent becomes confident of the wrong state with positive probability. In debates with multiple issues, the agent’s determination of favored and unfavored sources is disproportionately influenced by highly contentious topics which ultimately skew her posterior belief. Several learning applications illuminate the model’s predictions. Communicating networks of agents reach consensus faster on account of dissonance reduction. A prospective agent seeks out additional information, anticipating her ability to mold the new information in a way that, on average, bolsters perceived agreement. A strategic principal warps her desired message and engages in flattery to influence a dissonance-reducing agent.
Gender Differences in Competition: Evidence from Jeopardy! With Keith Chauvin and Anna Hopper.
We investigate the impace 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 critial 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. Paper available upon request.
Trade-Restricted and Non-Linear Competitive Equilibria.
In thin markets, competitive equilibrium may fail to exist when traders' preferences include complementarities. Such preferences induce discontinuitives in aggregate demand that can preclude market clearing. This kind of equilibrium breakdown is relevant for markets in which a small set of firms seek to acquire bundles of small, highly idiosyncratic goods. However, even when no competitive price vector exists, efficient trades may be supported by using non-linear prices or by restricting traders to a subset of exchange bids. This paper shows that these two alternative concepts are nearly equivalent in supportive power. Furthermore, restricted equilibria admit a natural hierarchy in which relatively less restrictive equilibria yield greater efficiency and satisfy tighter core conditions than their more restrictive counterparts. These generalized concepts may facilitate the development of price-based combinatorial exchanges. Paper available upon request.
Work in Progress:
Inference Consequences of Selection Neglect.
Population Games with Social Analogies.
Free Speaking Among Experts.
Empirical Evidence of Non-Equilibrium Wagering Behavior on Jeopardy!