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Anonymous social influence

Author

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  • FÖRSTER, Manuel

    (Université Paris 1 Panthéon-Sorbonne, France; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • GRABISCH, Michel

    (Paris School of Economics, Université Paris 1 Panthéon-Sorbonne, France)

  • RUSINOWSKA, Agnieszka

    (Paris School of Economics, CNRS, France)

Abstract

We study a stochastic model of influence where agents have “yes” or “no” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents share an opinion. For instance, this allows to study situations where the influence process is based on majorities, which are not covered by the classical approach of weighted averaging aggregation. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Our results can also be used to understand more general situations, where ordered weighted averaging operators are only used to some extend. We provide an analysis of the speed of convergence and the possible outcomes of the process. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like “most” or “at least a few”.

Suggested Citation

  • FÖRSTER, Manuel & GRABISCH, Michel & RUSINOWSKA, Agnieszka, 2013. "Anonymous social influence," LIDAM Discussion Papers CORE 2013028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2013028
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    References listed on IDEAS

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    1. 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.
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    6. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
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    16. 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.
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    Cited by:

    1. Michel Grabisch & Agnieszka Rusinowska, 2020. "A Survey on Nonstrategic Models of Opinion Dynamics," Games, MDPI, vol. 11(4), pages 1-29, December.
    2. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    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. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    5. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining influential models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01318081, HAL.
    6. Michel Grabisch & Agnieszka Rusinowska & Xavier Venel, 2019. "Diffusion in countably infinite networks," Documents de travail du Centre d'Economie de la Sorbonne 19017, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Documents de travail du Centre d'Economie de la Sorbonne 19024, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    8. GRABISCH, Michel & RUSINOWSKA, Agnieszka & VENEL, Xavier, 2022. "Diffusion in large networks," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    9. Merlone, U. & Radi, D., 2014. "Reaching consensus on rumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 260-271.
    10. Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska & Emily Tanimura, 2015. "Strategic influence in social networks," Post-Print hal-01158168, HAL.
    11. 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.
    12. Cristina Pardo-Garcia & Jose Sempere-Monerris, 2015. "Equilibrium mergers in a composite good industry with efficiencies," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 6(1), pages 101-127, March.
    13. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02372486, HAL.
    14. Foerster, Manuel, 2019. "Dynamics of strategic information transmission in social networks," Theoretical Economics, Econometric Society, vol. 14(1), January.
    15. Michel Grabisch & Agnieszka Rusinowska & Xavier Venel, 2022. "Diffusion in large networks," Post-Print halshs-03688783, HAL.
    16. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Post-Print halshs-02372486, HAL.
    17. MLINAR, Tanja B. & CHEVALIER, Philippe, 2013. "Pooling in manufacturing: do opposites attract?," LIDAM Discussion Papers CORE 2013040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Poindron, Alexis, 2021. "A general model of binary opinions updating," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 52-76.

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    More about this item

    Keywords

    influence; anonymity; ordered weighted averaging operator; convergence; consensus; speed of convergence; fuzzy linguistic quantifier;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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