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Let f_{k}(n) be the maximum number of time steps taken to reach equilibriumby a system of n agents obeying the k-dimensional Hegselmann-Krause boundedconfidence 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-knownlower bound in all dimensions k >= 2.

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