An improved energy argument for the Hegselmann-Krause model

TL;DR

This paper improves the upper bound on the freezing time of the Hegselmann-Krause model in higher dimensions, showing it is O(n^4) for n agents, which advances understanding of the model's convergence behavior.

Contribution

The paper presents a new upper bound on the freezing time of the Hegselmann-Krause model in dimensions two and higher, improving previous results.

Findings

Freezing time is O(n^4) for the d-dimensional model.

Improves the known upper bounds for dimensions d ≥ 2.

Provides insights into the convergence rate of the model.

Abstract

We show that the freezing time of the $d$-dimensional Hegselmann-Krause model is $O(n^4)$ where $n$ is the number of agents. This improves the best known upper bound whenever $d\geq 2$.