Dynamics of consensus formation on multiplex networks: The majority-vote model

Majority-vote model is a much-studied model for social opinion dynamics of two competing opinions. With the recent appreciation that our social network comprises a variety of different "layers" forming a multiplex network, a natural question arises on how such multiplex interactions affect the social opinion dynamics and consensus formation. Here, the majority-vote model will be studied on multiplex networks to understand the effect of multiplexity on opinion dynamics. We will discuss how global consensus is reached by three different types of voters-the normal, AND- and OR-rule voters--and what different microscopic origins are working in these different types. The AND-model reaches the largest consensus below Q_c. However, it needs much longer time to reach consensus than other models and the consensus collapses abruptly in the vicinity of the critical point. The OR-model has smaller level of consensus than AND-rule but it reaches the consensus more quickly thanks to weak endurances. The OR-model exhibits more active dynamics with more opinion flips as well as more disagreements than the AND-model, which render its consensus transition continuous at the critical point. The numerical simulation results are supported by analytical calculations based on approximate master equation.