The Hegselmann-Krause dynamics on the circle converge

TL;DR

This paper proves the convergence of the Hegselmann-Krause opinion dynamics model when applied to a circular domain, extending existing Euclidean space convergence proofs to a torus setting.

Contribution

It provides the first proof of convergence for Hegselmann-Krause dynamics on a circle, adapting methods from Euclidean space.

Findings

Established convergence of the model on the circle

Modified existing Euclidean convergence proofs for the torus setting

First rigorous proof of this kind for circular domain

Abstract

We consider the Hegselmann-Krause dynamics on a one-dimensional torus and provide the first proof of convergence of this system. The proof requires only fairly minor modifications of existing methods for proving convergence in Euclidean space.