# Spatial Opinion Dynamics and the Effects of Two Types of Mixing

## TL;DR

This paper investigates how different types of mixing, such as relocation and non-local interaction, influence opinion patterns like polarization and deadlock in spatial opinion dynamics models, revealing that mixing can break deadlock and hasten consensus.

## Contribution

It introduces two mixing mechanisms into spatial opinion models and analyzes their contrasting effects on opinion patterns, including deadlock and polarization.

## Key findings

- Mixing mechanisms can break deadlock and reduce polarization.
- Telephoning accelerates consensus formation.
- Relocation has a more pronounced effect than telephoning.

## Abstract

Spatially-situated opinions that can be held with different degrees of conviction lead to spatio-temporal patterns such as clustering (homophily), polarization, and deadlock. Our goal is to understand how sensitive these patterns are to changes in the local nature of interactions. We introduce two different mixing mechanisms, spatial relocation and non-local interaction ("telephoning"), to an earlier fully spatial model (no mixing). Interestingly, the mechanisms that create deadlock in the fully spatial model have the opposite effect when there is a sufficient amount of mixing. With telephoning, not only is polarization and deadlock broken up, but consensus is hastened. The effects of mixing by relocation are even more pronounced. Further insight into these dynamics is obtained for selected parameter regimes via comparison to the mean-field differential equations.