A particle method for continuous Hegselmann-Krause opinion dynamics

We derive a differential-integral equation akin to the Hegselmann-Krause model of opinion dynamics, and propose a particle method for solving the equation. Numerical experiments demonstrate second-order convergence of the method in a weak sense. We also show that our differential-integral equation c...

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Bibliographic Details
Main Authors Boghosian, Bruce, Börgers, Christoph, Dragovic, Natasa, Haensch, Anna, Kirshtein, Arkadz
Format Journal Article
LanguageEnglish
Published 11.11.2022
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Physics - Physics and Society
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Summary:We derive a differential-integral equation akin to the Hegselmann-Krause model of opinion dynamics, and propose a particle method for solving the equation. Numerical experiments demonstrate second-order convergence of the method in a weak sense. We also show that our differential-integral equation can equivalently be stated as a system of differential equations. An integration-by-parts argument that would typically yield an energy dissipation inequality in physical problems then yields a concentration inequality, showing that a natural measure of concentration increases monotonically.
DOI:10.48550/arxiv.2211.06265