Naive Bayesian Learning in Social Networks

TL;DR

This paper introduces a model of social learning that combines Bayesian updating with naive independence assumptions, capturing how agents communicate confidence and reach consensus or not, with applications to technology adoption.

Contribution

It proposes a novel model integrating Bayesian and naive learning, explicitly accounting for signal informativeness and communication of confidence in social networks.

Findings

Agents reach consensus under mild conditions.

Consensus can be explicitly computed using centrality and informativeness.

Information seeding in clusters can be effective if beliefs are expressively communicated.

Abstract

The DeGroot model of naive social learning assumes that agents only communicate scalar opinions. In practice, agents communicate not only their opinions, but their confidence in such opinions. We propose a model that captures this aspect of communication by incorporating signal informativeness into the naive social learning scenario. Our proposed model captures aspects of both Bayesian and naive learning. Agents in our model combine their neighbors' beliefs using Bayes' rule, but the agents naively assume that their neighbors' beliefs are independent. Depending on the initial beliefs, agents in our model may not reach a consensus, but we show that the agents will reach a consensus under mild continuity and boundedness assumptions on initial beliefs. This eventual consensus can be explicitly computed in terms of each agent's centrality and signal informativeness, allowing joint effects to be precisely understood. We apply our theory to adoption of new technology. In contrast to Banerjee et al. [2018], we show that information about a new technology can be seeded initially in a tightly clustered group without information loss, but only if agents can expressively communicate their beliefs.