Strong Convergence of a Random Actions Model in Opinion Dynamics

IF 3 3区计算机科学 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Signal and Information Processing over Networks Pub Date : 2024-02-01 DOI:10.1109/TSIPN.2024.3361373

Olle Abrahamsson;Danyo Danev;Erik G. Larsson

引用次数: 0

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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舆论动力学中随机行动模型的强收敛性

我们研究了一个舆论动态模型，在该模型中，每个代理都采取随机伯努利分布式行动，其概率在每个离散时间步中都会更新，我们证明了该模型几乎肯定会收敛到共识。我们还对文献中声称的这一结果的证明进行了详细批判。我们通过证明原始模型中的不可还原性假设并非必要，从而推广了这一结果。此外，作为广义结果的一个推论，我们还证明了在存在永不改变意见的顽固代理的情况下，几乎肯定会趋同于共识也是成立的。此外，我们还证明，无论是原始模型还是广义模型，都能以 $r$th 平均值收敛到共识。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Signal and Information Processing over Networks Computer Science-Computer Networks and Communications

CiteScore

5.80

自引率

12.50%

发文量

期刊介绍： The IEEE Transactions on Signal and Information Processing over Networks publishes high-quality papers that extend the classical notions of processing of signals defined over vector spaces (e.g. time and space) to processing of signals and information (data) defined over networks, potentially dynamically varying. In signal processing over networks, the topology of the network may define structural relationships in the data, or may constrain processing of the data. Topics include distributed algorithms for filtering, detection, estimation, adaptation and learning, model selection, data fusion, and diffusion or evolution of information over such networks, and applications of distributed signal processing.