On Convergence Rate of Scalar Hegselmann-Krause Dynamics

TL;DR

This paper establishes a tighter upper bound on the convergence time of the scalar Hegselmann-Krause opinion dynamics model, improving previous bounds from O(n^4) to O(n^3) using a novel analytical method.

Contribution

It introduces a new approach to analyze the convergence rate, reducing the upper bound from O(n^4) to O(n^3) for the model's termination time.

Findings

Convergence time is at most O(n^3)

Improves previous bound of O(n^4)

Uses a novel analytical method

Abstract

In this work, we derive a new upper bound on the termination time of the Hegselmann-Krause model for opinion dynamics. Using a novel method, we show that the termination rate of this dynamics happens no longer than $O(n^3)$ which improves the best known upper bound of $O(n^4)$ by a factor of $n$ .