Voter models and external influence

ABSTRACT

In this paper, we extend the voter model (VM) and the threshold voter model (TVM) to include external influences modeled 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 external influences in addition to local interactions.

KEYWORDS:

• Voter model
• threshold voter model
• opinion dynamics
• external influence
• mean field approximation
• diffusion approximation

Acknowledgement

RCT was supported by the Natural Sciences and Engineering Research Council (NSERC) Discovery Grant RGPIN-2016-05277. RCT and JRM also acknowledge the support of the UBC Okanagan Institute for Biodiversity, Resilience, and Ecosystem Services (BRAES). The authors would also like to thank anonymous reviewers for helpful comments.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.