Misinterpreting Others and the Fragility of Social Learning

Abstract

We exhibit a natural environment, social learning among heterogeneous agents, where even slight misperceptions can have a large negative impact on long‐run learning outcomes. We consider a population of agents who obtain information about the state of the world both from initial private signals and by observing a random sample of other agents' actions over time, where agents' actions depend not only on their beliefs about the state but also on their idiosyncratic types (e.g., tastes or risk attitudes). When agents are correct about the type distribution in the population, they learn the true state in the long run. By contrast, we show, first, that even arbitrarily small amounts of misperception about the type distribution can generate extreme breakdowns of information aggregation, where in the long run all agents incorrectly assign probability 1 to some fixed state of the world, regardless of the true underlying state. Second, any misperception of the type distribution leads long‐run beliefs and behavior to vary only coarsely with the state, and we provide systematic predictions for how the nature of misperception shapes these coarse long‐run outcomes. Third, we show that how fragile information aggregation is against misperception depends on the richness of agents' payoff‐relevant uncertainty; a design implication is that information aggregation can be improved by simplifying agents' learning environment. The key feature behind our findings is that agents' belief‐updating becomes “decoupled” from the true state over time. We point to other environments where this feature is present and leads to similar fragility results.

Learning With Heterogeneous Misspecified Models: Characterization and Robustness

“…Frick, Iijima, and Ishii (2020a) also demonstrated a failure of robustness in a social learning setting with an infinite state space and privately observed actions. In this environment, action choices are sensitive to small amounts of misspecification and agents with almost correct models can come to place probability 1 on an incorrect state.…”

“…They also establish that small errors on the part of a researcher in modeling or measuring biases will not significantly alter the predicted learning outcomes. In contrast, Frick, Iijima, and Ishii (2020a,b) showed that correctly specified environments are not robust in settings either with private actions and an infinite state space or which violate our uniformly informative actions assumption 6…”

“…In a variation of this canonical environment, underestimating redundant information leads to incorrect learning almost surely or cyclical learning (Gagnon‐Bartsch and Rabin (2016)). Misinterpreting others' preferences (Frick, Iijima, and Ishii (2020a)) and the gambler's fallacy (He (2020)) lead to incorrect learning almost surely; misinterpreting others' preferences can also lead to cyclical learning (Gagnon‐Bartsch (2016), Bohren and Hauser (2019)) or entrenched disagreement (Gagnon‐Bartsch (2016)) 7 . In contrast, coarse reasoning (Guarino and Jehiel (2013))—which also results in underestimating redundant information—or a linear updating heuristic that puts sufficient weight on agents' own signals (Jadbabaie et al (2012)) lead to correct learning almost surely.…”

“…3232 The total variation distance between distributions ψ and is . Pinsker's inequality implies that our results also hold for the Kullback–Leibler divergence, which has been used to study robustness in subsequent work (Frick, Iijima, and Ishii (2020a, 2020b)). …”

Projection of Private Values in Auctions

“…6 For instance, Goeree and Grosser (2007) explore the consequences of a false-consensus effect in two-party voting settings and show that voters' miscalculated probabilities of being pivotal can lead to inefficient election outcomes. More recently, Gagnon-Bartsch (2016), Bohren andHauser (2018), andIshii (2020) examine how misspecified beliefs about others' preferences interfere with social learning. Finally, Frick, Iijima, and Ishii (2019) show how the false-consensus effect may arise when agents neglect the assortative nature of matching when interacting with one another.…”