Consensus formation times in fully connected societies

Abstract

We developed a statistical mechanics approach to the problem of opinion formation in interacting agents, constrained by a set of social rules, $B$. To provide the agents with an adaptive quality, we represented both the social agents and the social rule by perceptrons. For fully connected societies we find that if the agents' interaction is weak, all agents adapt to the social rule $B$, with which they form a consensus; but if the interaction is sufficiently strong a consensus is built against the established $status$ $quo$. This behavior is observed for all temperatures $T$ and for all values of the agents' interaction parameter $H_{0}$, except in the limit $T\to\infty$ or when the interaction reaches the critical value $H_{0}=1,$ where no consensus is formed. The agents follow a path where, after a time $\alpha_{c},$ they disregard their peers' opinions on socially neutral issues and reach a full consensus at time $\alpha_{d}>\alpha_{c}.$ The measure of time $\alpha$ is proportional to the volume of information provided to the agents.