The role of fanatics in consensus formation

A model of opinion dynamics with two types of agents as social actors are presented, using the Ising thermodynamic model as the dynamics template. The agents are considered as opportunists which live at sites and interact with the neighbors, or fanatics/missionaries which move from site to site randomly in persuasion of converting agents of opposite opinion with the help of opportunists. Here, the moving agents act as an external influence on the opportunists to convert them to the opposite opinion. It is shown by numerical simulations that such dynamics of opinion formation may explain some details of consensus formation even when one of the opinions are held by a minority. Regardless the distribution of the opinion, different size societies exhibit different opinion formation behavior and time scales. In order to understand general behavior, the scaling relations obtained by comparing opinion formation processes observed in societies with varying population and number of randomly moving agents are studied. For the proposed model two types of scaling relations are observed. In fixed size societies, increasing the number of randomly moving agents give a scaling relation for the time scale of the opinion formation process. The second type of scaling relation is due to the size dependent information propagation in finite but large systems, namely finite-size scaling.