Fractal opinions among interacting agents
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913457702436864 |
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| author | Cao, Fei Cortez, Roberto |
| author_facet | Cao, Fei Cortez, Roberto |
| contents | We investigate an opinion model consisting of a large group of interacting agents, whose opinions are represented as numbers in $[-1,1]$. At each update time, two random agents are selected, and the opinion of the first agent is updated based on the opinion of the second (the ``persuader''). We derive the mean-field kinetic equation describing the large population limit of the model, and we provide several quantitative results establishing convergence to the unique equilibrium distribution. Surprisingly, in some range of the model parameters, the support of the equilibrium distribution exhibits a fractal structure. This provides a new mathematical description for the so-called opinion fragmentation phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01624 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractal opinions among interacting agents Cao, Fei Cortez, Roberto Probability Analysis of PDEs 91D25, 91D30, 82C31, 82C22, 35Q91, 35B40 We investigate an opinion model consisting of a large group of interacting agents, whose opinions are represented as numbers in $[-1,1]$. At each update time, two random agents are selected, and the opinion of the first agent is updated based on the opinion of the second (the ``persuader''). We derive the mean-field kinetic equation describing the large population limit of the model, and we provide several quantitative results establishing convergence to the unique equilibrium distribution. Surprisingly, in some range of the model parameters, the support of the equilibrium distribution exhibits a fractal structure. This provides a new mathematical description for the so-called opinion fragmentation phenomenon. |
| title | Fractal opinions among interacting agents |
| topic | Probability Analysis of PDEs 91D25, 91D30, 82C31, 82C22, 35Q91, 35B40 |
| url | https://arxiv.org/abs/2408.01624 |