Asynchronous Expressed and Private Opinion Dynamics on Influence Networks

Abstract

In this paper, we consider an asynchronous discrete-time opinion dynamics model for a social influence network, which consists of a population of interacting individuals, each holding a private and expressed opinion. At each time instant, a single individual activates and updates both her expressed and private opinions simultaneously. While an individual's new private opinion is shaped by her private opinion, the expressed opinions of her neighbors and attachment to an existing prejudice, her expressed opinion is instead a trade-off between her true private opinion and a “public opinion”, representing the current norm or standard opinion from the perspective of the individual. We show that the expressed and private opinions of all individuals converge to the same value exponentially fast when no individual holds an existing prejudice, with the lower bound on the convergence speed based on a general assumption on the network topology. If there are individuals who hold an existing prejudice, then the final opinions of every individual lie between the minimum and maximum value of those constant prejudices. Our results are also extended to consider the case where two or more individuals activate and update their opinions at each time instant. Simulations are provided to illustrate the results.