Stochastic model of agent interaction with opinion leaders

We analyze the problem of agents' interactions in a given population. The purpose of this paper is twofold. Starting from a scheme proposed by Galam [Physica A 320, 571 (2003)], which is based on a majority rule to treat the individuals' interactions, we first study some of its relevant properties. Then, we introduce special individuals, called opinion leaders, who play a key role in information spreading in several practical applications. Opinion leaders have the special feature of strongly interfering with the process based on the majority rule, speeding up the diffusion. We consider a model describing agents' interactions, which encompasses Galam's proposal, where opinion leaders are included as special agents. Then we study its specific properties which significantly recast and extend some conclusions drawn for the models given by Galam and Ellero, Fasano, and Sorato [Physica A 388, 3901 (2009)]. Finally, we provide theoretical and numerical results concerning the dynamics of our model, showing that a small percentage of opinion leaders may both accelerate and/or even reverse the overall consensus among all the agents.