A Proof of the Convergence of the Hegselmann-Krause Dynamics on the Circle

TL;DR

This paper provides a complete proof demonstrating that Hegselmann-Krause opinion dynamics systems converge when modeled on a circular domain, extending previous convergence results.

Contribution

It offers the first comprehensive proof of convergence for Hegselmann-Krause systems on the circle, based on established proof strategies.

Findings

Proves convergence of Hegselmann-Krause systems on the circle.

Extends convergence results from linear to circular domains.

Utilizes proof strategies from prior work by Hegarty, Martinsson, and Wedin.

Abstract

In this note, we give a complete proof that Hegselmann-Krause systems converge on the circle following the proof strategy developed by Hegarty, Martinsson, and Wedin.