Breaking Consensus in Kinetic Opinion Formation Models on Graphons

TL;DR

This paper introduces a control strategy to prevent consensus in large kinetic opinion models on graphons, effectively steering the system towards a declustered, diverse opinion state through analysis and numerical experiments.

Contribution

It develops a novel control approach for kinetic opinion models on graphons, analyzing its effectiveness in preventing consensus and promoting opinion diversity.

Findings

Control strategy effectively prevents consensus in various graphon structures.

Numerical experiments confirm the approach's ability to maintain opinion diversity.

Analysis of the Fokker-Planck equation shows long-term declustered states.

Abstract

In this work we propose and investigate a strategy to prevent consensus in kinetic models for opinion formation. We consider a large interacting agent system, and assume that agent interactions are driven by compromise as well as self-thinking dynamics and also modulated by an underlying static social network. This network structure is included using so-called graphons, which modulate the interaction frequency in the corresponding kinetic formulation. We then derive the corresponding limiting Fokker Planck equation, and analyze its large time behavior. This microscopic setting serves as a starting point for the proposed control strategy, which steers agents away from mean opinion and is characterised by a suitable penalization depending on the properties of the graphon. We show that this minimalist approach is very effective by analyzing the quasi-stationary solutions mean-field model in a plurality of graphon structures. Several numerical experiments are also provided to show the effectiveness of the approach in preventing the formation of consensus steering the system towards a declustered state.