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Analytical results for the Sznajd model of opinion formation

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  • F. Slanina
  • H. Lavicka

Abstract

The Sznajd model, which describes opinion formation and social influence, is treated analytically on a complete graph. We prove the existence of the phase transition in the original formulation of the model, while for the Ochrombel modification we find smooth behaviour without transition. We calculate the average time to reach the stationary state as well as the exponential tail of its probability distribution. An analytical argument for the observed 1/n dependence in the distribution of votes in Brazilian elections is provided. Copyright Springer-Verlag Berlin/Heidelberg 2003

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  • 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.
    • Handle: RePEc:spr:eurphb:v:35:y:2003:i:2:p:279-288
    DOI: 10.1140/epjb/e2003-00278-0
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    Cited by:

    1. Pérez-Llanos, Mayte & Pinasco, Juan Pablo & Saintier, Nicolas, 2020. "Opinion attractiveness and its effect in opinion formation models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    2. Guzmán-Vargas, L. & Hernández-Pérez, R., 2006. "Small-world topology and memory effects on decision time in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 372(2), pages 326-332.
    3. Düring, B. & Toscani, G., 2007. "Hydrodynamics from kinetic models of conservative economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 493-506.
    4. Sven Banischa & Ricardo Lima & Tanya Araújo, 2012. "Agent based models and opinion dynamics as markov chains," Working Papers Department of Economics 2012/10, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    5. Piotr Przybyła & Katarzyna Sznajd-Weron & Rafał Weron, 2014. "Diffusion Of Innovation Within An Agent-Based Model: Spinsons, Independence And Advertising," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-22.
    6. Czaplicka, Agnieszka & Charalambous, Christos & Toral, Raul & San Miguel, Maxi, 2022. "Biased-voter model: How persuasive a small group can be?," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    7. Grabowski, Andrzej, 2009. "Opinion formation in a social network: The role of human activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 961-966.
    8. Fang, Siwei & Zhao, Nan & Chen, Nan & Xiong, Fei & Yi, Yunhui, 2019. "Analyzing and predicting network public opinion evolution based on group persuasion force of populism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 809-824.
    9. Shang, Lihui & Zhao, Mingming & Ai, Jun & Su, Zhan, 2021. "Opinion evolution in the Sznajd model on interdependent chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    10. Galam, Serge, 2010. "Public debates driven by incomplete scientific data: The cases of evolution theory, global warming and H1N1 pandemic influenza," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3619-3631.
    11. Bertram During & Nicos Georgiou & Enrico Scalas, 2016. "A stylized model for wealth distribution," Papers 1609.08978, arXiv.org, revised Jul 2021.
    12. Zhong, Yue & Lai, Shaoyong & Hu, Chunhua, 2021. "Investigations to the dynamics of wealth distribution in a kinetic exchange model," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    13. Sznajd-Weron, Katarzyna & Sznajd, Józef & Weron, Tomasz, 2021. "A review on the Sznajd model — 20 years after," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    14. Pawel Sobkowicz, 2009. "Modelling Opinion Formation with Physics Tools: Call for Closer Link with Reality," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-11.
    15. Grabowski, A. & Kosiński, R.A., 2006. "Ising-based model of opinion formation in a complex network of interpersonal interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 651-664.
    16. Jin, Cheng & Li, Yifu & Jin, Xiaogang, 2017. "Political opinion formation: Initial opinion distribution and individual heterogeneity of tolerance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 257-266.

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