The diffusion of opposite opinions in a randomly biased environment

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 as on its own trend characteristic. The influence of the population trend can be positive, negative, or nonexistent in a random form. We prove a phase transition in the behavior of the proportion of each opinion. Specifically, the mean square proportions are linear functions of time in the diffusive case but are given by a power law in the superdiffusive regime. Published under license by AIP Publishing.