Partisan voter model: noise-induced transitions

Abstract

[eng] In this work we study the partisan voter model, an extension of the voter model in which each agent has an innate and fixed preference for one of two possible states. We study the model analytically on the complete graph using mean-field theory. The inclusion of preference implies the existence of a deterministic solution that does not exist in the classical voter model. In the mean-field limit, the system evolves to a situation in which agents tend to be in their preferred state. For a finite number of agents, relevant observables of the model have been studied going beyond what has been studied in the literature. Importantly, we demonstrate that the average time to reach one of the consensus states depends exponentially with the system size when it is large. In addition, we introduce the noisy partisan voter model, which adds idiosyncratic choices to the previous model. We assess the role that preference plays in the stationary probability distribution finding a new noise-induced transition. The stationary state of the system passes from a bimodal to a unimodal distribution through a trimodal distribution.