The Robustness of Consensus in Network-Based Non-Bayesian Learning Models

Abstract

This paper provides a formal characterization of non-Bayesian updating functions that yield asymptotic consensus in strongly connected networks. Extreme reluctance, a property of opinion formation that has been experimentally validated recently by Lorenz, Rauhut, Schweitzer and Helbing (2011) is shown to be crucial for asymptotic consensus.The paper further analyzes the robustness of asymptotic consensus when agents are subject to probabilistic mistakes while forming their opinions. A sufficient condition on the stochastic process of errors is characterized such that asymptotic consensus holds almost surely.As corollaries of the general theorems, new results to the literature on (i) political opinion formation with partisans, and (ii) cognitive dissonance are provided. Partisan and/or cognitive dissonant agents do not perpetuate sharp differences of opinions within social networks. Despite their presence, asymptotic consensus occurs in strongly connected networks.