A straightforward proof of the critical value in the Hegselmann-Krause model: up to one-half

Hsin-Lun Li

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arXiv · 2408.03718

A straightforward proof of the critical value in the Hegselmann-Krause model: up to one-half

Hsin-Lun Li

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Abstract

In the Hegselmann-Krause model, an agent updates its opinion by averaging with others whose opinions differ by at most a given confidence threshold. With agents' initial opinions uniformly distributed on the unit interval, we provide a straightforward proof that establishes the critical value is up to one-half. This implies that the probability of consensus approaches one as the number of agents tends to infinity for confidence thresholds larger than or equal to one-half.

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Hsin-Lun Li. 2024-08-07. A straightforward proof of the critical value in the Hegselmann-Krause model: up to one-half. https://arxiv.org/abs/2408.03718

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