Dynamic Opinion Aggregation: Long-Run Stability and Disagreement.

This article develops a general model of non-Bayesian social learning in networks through *robust opinion aggregators*, which are non-linear updating rules characterized by normalization, monotonicity, and translation invariance. It introduces two associated network structures—*strong* and *weak ties*—that capture minimal and maximal influence among agents, respectively, and provides graph-theoretic conditions under which opinions converge, consensus forms, or persistent disagreement arises. The model generalizes the classical DeGroot linear updating rule by allowing agents to selectively weigh or ignore neighbors' opinions based on current profiles, thereby explaining phenomena such as polarization and opinion segregation. For large populations, the article establishes necessary and sufficient conditions for the *wisdom of the crowd*—the convergence of aggregate opinions to the true underlying parameter—expressed in terms of the strong and weak influence vectors and the connectivity of the weak network, with applications to various network topologies including Erdös–Rényi and expander graphs. Finally, it provides a microfoundation for robust opinion aggregators as solutions to distance-minimization problems with loss functions, linking the updating dynamics to repeated estimation and best-response behavior in coordination games.