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arXiv · 2401.16574

Strong Convergence of a Random Actions Model in Opinion Dynamics

Olle Abrahamsson·Danyo Danev·Erik G. Larsson
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Abstract

We study an opinion dynamics model in which each agent takes a random Bernoulli distributed action whose probability is updated at each discrete time step, and we prove that this model converges almost surely to consensus. We also provide a detailed critique of a claimed proof of this result in the literature. We generalize the result by proving that the assumption of irreducibility in the original model is not necessary. Furthermore, we prove as a corollary of the generalized result that the almost sure convergence to consensus holds also in the presence of a stubborn agent which never changes its opinion. In addition, we show that the model, in both the original and generalized cases, converges to consensus also in $r$th mean.

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Olle Abrahamsson, Danyo Danev, Erik G. Larsson. 2024-01-29. Strong Convergence of a Random Actions Model in Opinion Dynamics. https://arxiv.org/abs/2401.16574

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