Noise-driven bias in the non-local voter model

Abstract

Is it more effective to have a strong influence over a small domain, or a weaker influence over a larger one? Here, we introduce and analyse an off-lattice generalisation of the voter model, in which the range and strength of agents' influence are control parameters. We consider both low and high density regimes and, using distinct mathematical approaches, derive analytical predictions for the evolution of agent densities. We find that, even when the agents are equally persuasive on average, those whose influence is wider but weaker have an overall noise-driven advantage allowing them to reliably dominate the entire population. We discuss the implications of our results and the potential of our model (or adaptations thereof) to improve the understanding of political campaign strategies and the evolution of disease.