Robust Opinion Aggregation and its Dynamics

We study agents in a social network who receive initial noisy signals about a fundamental parameter and then, in each period, solve a robust non-parametric estimation problem given their previous information and the most recent estimates of their neighbors. The resulting robust opinion aggregators are characterized by simple functional properties: normalization, monotonicity, and translation invariance. These aggregators admit the linear DeGroot's model as a particular parametric specification. However, robust opinion aggregators allow for additional features such as overweighting/underweighting of extreme opinions, confirmatory bias, as well as discarding information obtained from sources perceived as redundant. We show that under this general model, it is still possible to link the long-run behavior of the opinions to the structure of the underlying network. In particular, we provide sufficient conditions for convergence and consensus and we offer some bounds on the rate of convergence. In some parametric cases, we derive the influence of the agents on the limit opinions and we stress how it depends on their centrality as well as on their initial signals. Finally, we study sufficient conditions under which a large society learns the true parameter while also highlighting why this property may fail.