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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.21081 |
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| _version_ | 1866911535117369344 |
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| author | Abedinzadeh, M. Hossein Akyol, Emrah |
| author_facet | Abedinzadeh, M. Hossein Akyol, Emrah |
| contents | We study multidimensional opinion dynamics under confirmation bias in social networks. Each agent holds a vector of correlated opinions across multiple topic layers. Peer interaction is modeled through a static, informationally symmetric social channel, while external information enters through a dynamic, informationally asymmetric source channel. Source influence is described by nonnegative state-dependent functions of agent--source opinion mismatch, which captures confirmation bias without hard thresholds. For general Lipschitz source-influence functions, we give sufficient conditions under which the dynamics are contractive and converge to a unique steady state independent of the initial condition. For affine confirmation-bias functions, we show that the steady state can be computed through a finite sign-consistency search and identify a regime in which it admits a closed form. For broader classes of bounded nonlinear source-influence functions, we derive explicit lower and upper bounds on the fixed point. Numerical examples and a study on a real-world adolescent lifestyle network illustrate the role of multidimensional coupling and show that source-design conclusions can change qualitatively when confirmation bias is ignored. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21081 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multidimensional Opinion Dynamics with Confirmation Bias: A Multi-Layer Framework Abedinzadeh, M. Hossein Akyol, Emrah Systems and Control Dynamical Systems We study multidimensional opinion dynamics under confirmation bias in social networks. Each agent holds a vector of correlated opinions across multiple topic layers. Peer interaction is modeled through a static, informationally symmetric social channel, while external information enters through a dynamic, informationally asymmetric source channel. Source influence is described by nonnegative state-dependent functions of agent--source opinion mismatch, which captures confirmation bias without hard thresholds. For general Lipschitz source-influence functions, we give sufficient conditions under which the dynamics are contractive and converge to a unique steady state independent of the initial condition. For affine confirmation-bias functions, we show that the steady state can be computed through a finite sign-consistency search and identify a regime in which it admits a closed form. For broader classes of bounded nonlinear source-influence functions, we derive explicit lower and upper bounds on the fixed point. Numerical examples and a study on a real-world adolescent lifestyle network illustrate the role of multidimensional coupling and show that source-design conclusions can change qualitatively when confirmation bias is ignored. |
| title | Multidimensional Opinion Dynamics with Confirmation Bias: A Multi-Layer Framework |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2603.21081 |