A Stochastic Model of Diffusion in Opinion Dynamics

This paper studies analytically the dynamics of the opinion in multi-agent systems when only the sociological phenomenon known as diffusion is considered. First, the paper recalls a framework for the analytic study of opinion dynamics which has been already applied to describe the effects of a number of sociological phenomena. Then, the framework is specialized to the study of diffusion, according to which the opinion of an agent can be influenced by the social context. Diffusion is introduced in the framework by stating stochastic rules meant to describe at the microscopic level how diffusion contributes to change the opinion of an agent. The obtained model is used to derive collective and asymptotic properties of multi-agent systems when only diffusion is considered, which are verified against specific simulations shown in the last part of the paper. The paper is concluded with a recapitulation of presented results and an outline of future work.