The diffusion of opposite opinions in a randomly biased environment

Abstract

We propose a model for diffusion of two opposite opinions. Here, the decision to be taken by each individual is a random variable which depends on the tendency of the population, as well on its own trend characteristic. The influence of the population trend can be positive, negative or non-existent in a random form. We prove a phase transition in the behaviour of the proportion of each opinion. Namely, the mean square proportions are linear functions of time in the diffusive case, but are given by a power law in the superdiffusive regime.