This article proposes a model of non-Bayesian social learning in networks that accounts for heuristics and biases in opinion aggregation. The updating rules are represented by non-linear opinion aggregators from which we extract two extreme networks capturing strong and weak links. We provide graph-theoretic conditions for these networks that characterize opinions’ convergence, consensus formation, and efficient or biased information aggregation. Under these updating rules, agents may ignore some of their neighbours’ opinions, reducing the number of effective connections and inducing long-run disagreement for finite populations. For the wisdom of the crowd in large populations, we highlight a trade-off between how connected the society is and the non-linearity of the opinion aggregator. Our framework bridges several models and phenomena in the non-Bayesian social learning literature, thereby providing a unifying approach to the field.

We study agents who are more likely to remember some experiences than others but update beliefs as if the experiences they remember are the only ones that occurred. To understand the long-run effects of selective memory, we propose selective-memory equilibrium. We show that if the agent’s behavior converges, their limit strategy is a selective-memory equilibrium, and we provide a sufficient condition for behavior to converge. We use this equilibrium concept to explore the consequences of several well-documented biases. We also show that there is a close connection between selective-memory equilibria and the outcomes of misspecified learning.