On the Evolution of Public Opinion in the Presence of Confirmation BIAS

This paper provides a model to investigate the evolution of opinions in social networks comprising of individuals and other influential entities, which herein are referred to as information sources. Each individual holds an opinion represented by a scalar that evolves over time. The information sources are stubborn, in the sense that their opinions are time-invariant. Individuals receive the opinions of information sources that are closer to their belief, confirmation bias is explicitly incorporated into the model. The proposed dynamics of the social network is adopted from DeGroot-Friedkin model, where an individual's opinion update mechanism is a convex combination of her innate opinion, her neighbors' opinions at the previous time step, and the opinions passed along by information sources which she follows. In our specific model, the social network relies on trust and hence static, while the information sources are highly dynamic since they are weighted as a function of the distance between an individual state and the state of information source to account for confirmation bias. The conditions for convergence of the aforementioned dynamics to a unique equilibrium point are characterized. The estimation and exact computation of the steady-state values under non-linear and linear state-dependent weight functions are provided. Finally, the impact of the distance between polarized opinions of information sources in the public opinion evolution is numerically analyzed in the context of the well-known Krackhardt's advice network.