Information cascade on networks and phase transitions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916337803067392 |
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| author | Hisakado, Masato Nakayama, Kazuaki Mori, Shintaro |
| author_facet | Hisakado, Masato Nakayama, Kazuaki Mori, Shintaro |
| contents | Herein, we consider a voting model for information cascades on several types of networks -- a random graph, the Barabási-Albert(BA) model, and lattice networks -- by using one parameter $ω$; $ω=1,0, -1$ respectively correspond to these networks. $ω$ is related to the size of hubs. We discuss the differences between the phases in which the networks depend. In $ω\ne -1$, without, the following two types of phase transitions can be observed: information cascade transition and super-normal transition. The first is the transition between a state where most voters make correct choices and a state where most of them are wrong. This is an absorption transition that belongs to the non-equilibrium transition. In the symmetric case, the phase transition is continuous and the universality class is the same as nonlinear Pólya model. In contrast, in the asymmetric case, there is a discontinuous phase transition, where the gap depends on the network. The super-normal transition is the transition of the convergence speed, and the critical point of the convergence speed transition depends on $ω$. At $ω=1$, in the BA model, this transition disappears. Both phase transitions disappear at $ω=-1$ in the lattice case. In conclusion, as the performance near the lattice case, $ω\sim-1$ exhibits the best performance of the voting in all networks. As the hub size decreases, the performance improves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_12295 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Information cascade on networks and phase transitions Hisakado, Masato Nakayama, Kazuaki Mori, Shintaro Physics and Society Data Analysis, Statistics and Probability Herein, we consider a voting model for information cascades on several types of networks -- a random graph, the Barabási-Albert(BA) model, and lattice networks -- by using one parameter $ω$; $ω=1,0, -1$ respectively correspond to these networks. $ω$ is related to the size of hubs. We discuss the differences between the phases in which the networks depend. In $ω\ne -1$, without, the following two types of phase transitions can be observed: information cascade transition and super-normal transition. The first is the transition between a state where most voters make correct choices and a state where most of them are wrong. This is an absorption transition that belongs to the non-equilibrium transition. In the symmetric case, the phase transition is continuous and the universality class is the same as nonlinear Pólya model. In contrast, in the asymmetric case, there is a discontinuous phase transition, where the gap depends on the network. The super-normal transition is the transition of the convergence speed, and the critical point of the convergence speed transition depends on $ω$. At $ω=1$, in the BA model, this transition disappears. Both phase transitions disappear at $ω=-1$ in the lattice case. In conclusion, as the performance near the lattice case, $ω\sim-1$ exhibits the best performance of the voting in all networks. As the hub size decreases, the performance improves. |
| title | Information cascade on networks and phase transitions |
| topic | Physics and Society Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2302.12295 |