Voter Models and External Influence

TL;DR

This paper extends voter models to include external influences modeled as jump processes, analyzing their impact on consensus probability and time through analytical and computational methods.

Contribution

It introduces external influences into voter models and provides analytical and computational analysis of their effects on consensus dynamics.

Findings

External influence accelerates consensus formation.

The effect of external influence is more significant in the voter model than in the threshold voter model.

External influences highlight macro-level phenomena over local interactions.

Abstract

In this paper, we extend the voter model (VM) and the threshold voter model (TVM) to include external influences modelled as a jump process. We study the newly-formulated models both analytically and computationally, employing diffusion approximations and mean field approximations. We derive results pertaining to the probability of reaching consensus on a particular opinion and also the expected consensus time. We find that although including an external influence leads to a faster consensus in general, this effect is more pronounced in the VM as compared to the TVM. Our findings suggest the potential importance of "macro-level" phenomena such as the external influences as compared to "micro-level" local interactions.