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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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    References listed on IDEAS

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    1. D. Stauffer & A. O. Sousa & S. Moss De Oliveira, 2000. "Generalization To Square Lattice Of Sznajd Sociophysics Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1239-1245.
    2. Katarzyna Sznajd-Weron & Józef Sznajd, 2000. "Opinion Evolution In Closed Community," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1157-1165.
    3. Andjel, Enrique D. & Liggett, Thomas M. & Mountford, Thomas, 1992. "Clustering in one-dimensional threshold voter models," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 73-90, August.
    4. F. Slanina & H. Lavicka, 2003. "Analytical results for the Sznajd model of opinion formation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 35(2), pages 279-288, September.
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