We present an approach to analyse learning outcomes in a broad class of misspecified environments, spanning both single-agent and social learning. We introduce a novel “prediction accuracy” order over subjective models and observe that this makes it possible to partially restore standard martingale convergence arguments that apply under correctly specified learning. Based on this, we derive general conditions to determine when beliefs in a given environment converge to some long-run belief either locally or globally (i.e. from some or all initial beliefs). We show that these conditions can be applied, first, to unify and generalize various convergence results in previously studied settings. Second, they enable us to analyse environments where learning is “slow”, such as costly information acquisition and sequential social learning. In such environments, we illustrate that even if agents learn the truth when they are correctly specified, vanishingly small amounts of misspecification can generate extreme failures of learning.
We formulate a model of social interactions and misinferences by agents who neglect assortativity in their society, mistakenly believing that they interact with a representative sample of the population. A key component of our approach is the interplay between this bias and agents' strategic incentives. We highlight a mechanism through which assortativity neglect, combined with strategic complementarities in agents' behavior, drives up action dispersion in society (e.g., socioeconomic disparities in education investment). We also suggest that the combination of assortativity neglect and strategic incentives may be relevant in understanding empirically documented misperceptions of income inequality and political attitude polarization.