Divergence and consensus in majority rule.

Abstract

We investigate majority rule dynamics in a population with two classes of people, each with two opinion states ±1, and with tunable interactions between people in different classes. In an update, a randomly selected group adopts the majority opinion if all group members belong to the same class; if not, majority rule is applied with rate ε. Consensus is achieved in a time that scales logarithmically with population size if ε≥ε_{c}=1/9. For ε<ε_{c}, the population can get trapped in a polarized state, with one class preferring the +1 state and the other preferring -1. The time to escape this polarized state and reach consensus scales exponentially with population size.