Strong Convergence of a Random Actions Model in Opinion Dynamics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916110120517632 |
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| author | Abrahamsson, Olle Danev, Danyo Larsson, Erik G. |
| author_facet | Abrahamsson, Olle Danev, Danyo Larsson, Erik G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong Convergence of a Random Actions Model in Opinion Dynamics Abrahamsson, Olle Danev, Danyo Larsson, Erik G. Social and Information Networks 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. |
| title | Strong Convergence of a Random Actions Model in Opinion Dynamics |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2401.16574 |