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arXiv · 2211.06265

A particle method for continuous Hegselmann-Krause opinion dynamics

Bruce Boghosian·Christoph Börgers·Natasa Dragovic·Anna Haensch·Arkadz Kirshtein
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Abstract

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.

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Bruce Boghosian, Christoph Börgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein. 2022-11-11. A particle method for continuous Hegselmann-Krause opinion dynamics. https://arxiv.org/abs/2211.06265

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