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Ordered Weighted Averaging in Social Networks

Author

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  • Manuel Förster

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, UCL - Université Catholique de Louvain)

  • Michel Grabisch

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

  • Agnieszka Rusinowska

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

Abstract

We study a stochastic model of influence where agents have yes-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. This allows to study situations where the influence process resembles a majority vote, which are not covered by the classical approach of weighted averaging aggregation. We provide an analysis of the speed of convergence and the probabilities of absoption by different terminal classes. We find a necessary and sufficient condition for convergence to consensus and characterize terminal states. Our results can also be used to understand more general situations, where ordered weighted averaging operators are only used to some extend. Furthermore, we apply our results to fuzzy linguistic quantifiers.

Suggested Citation

  • Manuel Förster & Michel Grabisch & Agnieszka Rusinowska, 2012. "Ordered Weighted Averaging in Social Networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00746988, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00746988
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00746988
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    References listed on IDEAS

    as
    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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    8. Jacek Malczewski & Claus Rinner, 2005. "Exploring multicriteria decision strategies in GIS with linguistic quantifiers: A case study of residential quality evaluation," Journal of Geographical Systems, Springer, vol. 7(2), pages 249-268, June.
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    Cited by:

    1. Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska & Emily Tanimura, 2015. "Strategic influence in social networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01158168, HAL.
    2. repec:the:publsh:3056 is not listed on IDEAS
    3. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining influential models," Documents de travail du Centre d'Economie de la Sorbonne 16038, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. 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.
    5. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    6. Michel Grabisch & Alexis Poindron & Agnieszka Rusinowka, 2017. "A model of anonymous influence with anti-conformist agents," Documents de travail du Centre d'Economie de la Sorbonne 17047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Merlone, U. & Radi, D., 2014. "Reaching consensus on rumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 260-271.
    8. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining models of influence," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 2, pages 69-85.
    9. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining models of influence," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 2, pages 69-85.
    10. MLINAR, Tanja B. & CHEVALIER, Philippe, 2013. "Pooling in manufacturing: do opposites attract?," CORE Discussion Papers 2013040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    Keywords

    fuzzy linguistic quantifier; social network; influence; convergence; speed of convergence; consensus; ordered weighted averaging operator; réseau social; vitesse de convergence; moyenne ordonnée pondérée; quantificateur linguistique flou;

    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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