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

TL;DR

This paper introduces a nonlinear voter model to analyze how herd behavior influences the speed of reaching global consensus across various network types, revealing an optimal herd effect parameter for fastest convergence.

Contribution

The study presents a novel nonlinear voter model with an adjustable herd behavior parameter, providing insights into consensus dynamics on different network structures.

Findings

Existence of an optimal herd effect parameter for fastest consensus.

Consensus speed varies with network topology.

Spatiotemporal analysis reveals opinion cluster evolution.

Abstract

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 $\alpha$ controls the effect of herd behavior on consensus. We find that there exists an optimal value of $\alpha$ 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.