Non-Bayesian Social Learning and the Spread of Misinformation in Networks

People are exposed to a constant flow of information about economic, social and political phenomena; nevertheless, misinformation is ubiquitous in the society. This paper studies the spread of misinformation in a social environment where agents receive new information each period and update their opinions taking into account both their experience and neighborhood's ones. I consider two types of misinformation: permanent and temporary. Permanent misinformation is modeled with the presence of stubborn agents in the network and produces long-run effects on the agents learning process. The distortion induced by stubborn agents in social learning depends on the "updating centrality", a novel centrality measure that identifies the key agents of a social learning process, and generalizes the Katz-Bonacich measure. Conversely, temporary misinformation, represented by shocks of rumors or fake news, has only short-run effects on the opinion dynamics. Results rely on spectral graph theory and show that the consensus among agents is not always a sign of successful learning. In particular, the consensus time is increasing with respect to the "bottleneckedness" of the underlying network, while the learning time is decreasing with respect to agents' reliance on their private signals.