The Hegselmann-Krause dynamics for continuous agents and a regular opinion function do not always lead to consensus

TL;DR

This paper provides a counterexample showing that the Hegselmann-Krause bounded confidence model can fail to reach consensus even with continuous opinions, confirming a prior conjecture.

Contribution

It constructs a specific regular opinion function demonstrating persistent opinion separation, confirming a conjecture about the limitations of the model.

Findings

Counterexample of persistent opinion separation

Confirms conjecture by Blondel, Hendrickx, and Tsitsiklis

Shows limitations of the Hegselmann-Krause model

Abstract

We present an example of a regular opinion function which, as it evolves in accordance with the discrete-time Hegselmann-Krause bounded confidence dynamics, always retains opinions which are separated by more than two. This confirms a conjecture of Blondel, Hendrickx and Tsitsiklis.