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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.16574 |
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Table of 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.