Dynamics of Non-Conservative Voters

TL;DR

This paper investigates opinion formation models where voters' alignment depends non-linearly on neighbors, revealing biases toward consensus or polarization, using approximations to predict final states.

Contribution

It introduces a non-linear voter model framework and applies a decoupling approximation to analyze the dynamics and final consensus probabilities.

Findings

Population can bias toward zero magnetization or consensus depending on non-linearity.

Average magnetization is generally not conserved in these models.

The approach extends to models with influence from distant voters, like the Sznajd model.

Abstract

We study a family of opinion formation models in one dimension where the propensity for a voter to align with its local environment depends non-linearly on the fraction of disagreeing neighbors. Depending on this non-linearity in the voting rule, the population may exhibit a bias toward zero magnetization or toward consensus, and the average magnetization is generally not conserved. We use a decoupling approximation to truncate the equation hierarchy for multi-point spin correlations and thereby derive the probability to reach a final state of a given consensus as a function of the initial magnetization. The case when voters are influenced by more distant voters is also considered by investigating the Sznajd model.