Convergence to global consensus in opinion dynamics under a nonlinear voter model

We propose a nonlinear voter model to study the emergence of global consensus in opinion dynamics. In our model, agent i agrees with one of binary opinions with the probability that is a power function of the number of agents holding this opinion among agent i and its nearest neighbors, where an adjustable parameter α controls the effect of herd behavior on consensus. We find that there exists an optimal value of α leading to the fastest consensus for lattices, random graphs, small-world networks and scale-free networks. Qualitative insights are obtained by examining the spatiotemporal evolution of the opinion clusters. -- Highlights: ► A nonlinear voter model with respect to degree of herd effect is proposed to study consensus dynamics on complex networks. ► It is found that suitable degree of herd effect can result in optimal convergence velocity toward the global consensus. ► The formation of opinion clusters affected by herd effect plays the key role in the acceleration of achieving global consensus.