Heterogeneous Voter Models

TL;DR

This paper introduces two new voter models that incorporate individual heterogeneity and fixed preferences, revealing longer consensus times and stable polarized states compared to classic models.

Contribution

The paper presents the heterogeneous voter model and partisan voter model, extending traditional voter models to include individual differences and fixed preferences.

Findings

Consensus time in HVM is significantly longer than in classic voter models.

PVM leads to stable polarized states aligned with individual preferences.

Finite populations eventually reach consensus, but the time scales exponentially with size.

Abstract

We introduce the heterogeneous voter model (HVM), in which each agent has its own intrinsic rate to change state, reflective of the heterogeneity of real people, and the partisan voter model (PVM), in which each agent has an innate and fixed preference for one of two possible opinion states. For the HVM, the time until consensus is reached is much longer than in the classic voter model. For the PVM in the mean-field limit, a population evolves to a "selfish" state, where each agent tends to be aligned with its internal preference. For finite populations, discrete fluctuations ultimately lead to consensus being reached in a time that scales exponentially with population size.