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A general model of synchronous updating with binary opinions

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  • Alexis Poindron

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

We consider a society of agents making an iterated yes/no decision on some issue, where updating is done by mutual influence under a Markovian process. Agents update their opinions at the same time, independently of each other, in an entirely mechanical manner. They can have a favourable or an unfavourable perception of their neighbours. We study the qualitative patterns of this model, which captures several notions, including conformism, anti-conformism, communitarianism and leadership. We discuss under which conditions opinions are stable. Finally, we introduce a notion of entropy that we use to extract information on the society and to predict future opinions.

Suggested Citation

  • Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Post-Print halshs-02372486, HAL.
    • Handle: RePEc:hal:journl:halshs-02372486
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02372486
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    References listed on IDEAS

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    1. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    2. Michel Grabisch & Fen Li, 2020. "Anti-conformism in the Threshold Model of Collective Behavior," Dynamic Games and Applications, Springer, vol. 10(2), pages 444-477, June.
    3. Grabisch, Michel & Poindron, Alexis & Rusinowska, Agnieszka, 2019. "A model of anonymous influence with anti-conformist agents," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    4. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    5. Michel Grabisch, 2016. "Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 301-326, July.
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    9. Serge Galam, 2008. "Sociophysics: A Review Of Galam Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 409-440.
    10. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining models of influence," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(2), pages 69-85.
    11. Yann Bramoullé & Dunia López-Pintado & Sanjeev Goyal & Fernando Vega-Redondo, 2004. "Network formation and anti-coordination games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 1-19, January.
    12. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, March.
    13. Manuel Förster & Michel Grabisch & Agnieszka Rusinowska, 2012. "Ordered Weighted Averaging in Social Networks," Documents de travail du Centre d'Economie de la Sorbonne 12056, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    15. 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.
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    Keywords

    opinion dynamics; convergence; absorbing class; groups; entropy;
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