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Consensus and stability in imitation-based binary opinion dynamics on social graphs

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  • Li, Hsin-Lun

Abstract

We present three imitation models with binary opinions: Models A, B, and C. Models A and B are inspired by the Sznajd model, while Model C is inspired by the threshold voter model. Unlike the original Sznajd model, which was investigated on a linear chain, our imitation models can be applied to any finite social graph. In Model A, a pair of socially connected agents holding the same opinion causes their social neighbors to adopt the same opinion. Model A evolves into Model B if a pair of socially connected agents with distinct opinions leads to disagreements among their non-common social neighbors. In Model C, an agent has the opportunity to alter its opinion when its opposing social neighbors constitute either the majority or the minority. We demonstrate that convergence is guaranteed in Models A and B. In Model C, there is almost surely no consensus if an agent has a chance of changing its opinion when its opposing social neighbors are in the minority.

Suggested Citation

  • Li, Hsin-Lun, 2025. "Consensus and stability in imitation-based binary opinion dynamics on social graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 676(C).
    • Handle: RePEc:eee:phsmap:v:676:y:2025:i:c:s0378437125005205
    DOI: 10.1016/j.physa.2025.130868
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