Spread of Information With Confirmation Bias in Cyber-Social Networks

Abstract

This paper provides a model to investigate information spread over cyber-social network of agents. The cyber-social network considered here comprises individuals and 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 cyber-social networks 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 (obtained from the social network), and the opinions passed along by information sources from cyber layer which she follows. The characteristics of the interdependent social and cyber networks are significantly different here: the social network relies on trust and hence static, while influences from information sources to individuals 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 polarization in the opinions of information sources on the public opinion evolution is numerically analyzed in the context of the well-known Krackhardt's advice network.