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arXiv · 1211.1909

On the Convergence of the Hegselmann-Krause System

Arnab Bhattacharyya·Mark Braverman·Bernard Chazelle·Huy L. Nguyen
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Abstract

We study convergence of the following discrete-time non-linear dynamical system: n agents are located in R^d and at every time step, each moves synchronously to the average location of all agents within a unit distance of it. This popularly studied system was introduced by Krause to model the dynamics of opinion formation and is often referred to as the Hegselmann-Krause model. We prove the first polynomial time bound for the convergence of this system in arbitrary dimensions. This improves on the bound of n^{O(n)} resulting from a more general theorem of Chazelle. Also, we show a quadratic lower bound and improve the upper bound for one-dimensional systems to O(n^3).

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Arnab Bhattacharyya, Mark Braverman, Bernard Chazelle, Huy L. Nguyen. 2012-11-08. On the Convergence of the Hegselmann-Krause System. https://arxiv.org/abs/1211.1909

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