A Comment on and Correction to: Opinion dynamics in the presence of increasing agreement pressure

TL;DR

This paper corrects a previous opinion dynamics model by providing a new fixed point theorem-based condition that ensures consensus under increasing peer-pressure, addressing a counter-example and validating earlier claims.

Contribution

It introduces a novel variation of the Banach Fixed Point theorem to resolve a counter-example and establish a sufficient condition for consensus in opinion dynamics models.

Findings

Identifies a counter-example to previous consensus results.

Proposes a new fixed point theorem-based condition for consensus.

Validates earlier claims under the new sufficient condition.

Abstract

We identify a counter-example to the consensus result given in [J. Semonsen et al. Opinion dynamics in the presence of increasing agreement pressure. \textit{IEEE Trans. Cyber.}, 49(4): 1270-1278, 2018]. We resolve the counter-example by replacing Lemma 5 in the given reference with a novel variation of the Banach Fixed Point theorem which explains both the numerical results in the reference and the counter-example(s) in this note, and provides a sufficient condition for consensus in systems with increasing peer-pressure. This work is relevant for other papers that have used the proof technique from Semonsen et al. and establishes the veracity of their claims assuming the new sufficient condition.