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arXiv · 1406.0769

A quadratic lower bound for the convergence rate in the one-dimensional Hegselmann-Krause bounded confidence dynamics

Edvin Wedin·Peter Hegarty
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Abstract

Let f_{k}(n) be the maximum number of time steps taken to reach equilibrium by a system of n agents obeying the k-dimensional Hegselmann-Krause bounded confidence dynamics. Previously, it was known that \Omega(n) = f_{1}(n) = O(n^3). Here we show that f_{1}(n) = \Omega(n^2), which matches the best-known lower bound in all dimensions k >= 2.

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Edvin Wedin, Peter Hegarty. 2014-06-02. A quadratic lower bound for the convergence rate in the one-dimensional Hegselmann-Krause bounded confidence dynamics. https://arxiv.org/abs/1406.0769

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