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Anonymous social influence

Author

Listed:
  • 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

    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.
    2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    3. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    4. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
    5. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
    6. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    7. Andrea Galeotti & Sanjeev Goyal, 2009. "Influencing the influencers: a theory of strategic diffusion," RAND Journal of Economics, RAND Corporation, vol. 40(3), pages 509-532, September.
    8. Venkatesh Bala & Sanjeev Goyal, 1998. "Learning from Neighbours," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 595-621.
    9. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    10. Banerjee, Abhijit & Fudenberg, Drew, 2004. "Word-of-mouth learning," Games and Economic Behavior, Elsevier, vol. 46(1), pages 1-22, January.
    11. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
    12. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, and Unidimensional Opinions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 909-968.
    13. 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.
    14. López-Pintado, Dunia, 2008. "Diffusion in complex social networks," Games and Economic Behavior, Elsevier, vol. 62(2), pages 573-590, March.
    15. Goyal, Sanjeev & Galeotti, Andrea, 2007. "A Theory of Strategic Diffusion," Coalition Theory Network Working Papers 9096, Fondazione Eni Enrico Mattei (FEEM).
    16. Buechel, Berno & Hellmann, Tim & Pichler, Michael M., 2014. "The dynamics of continuous cultural traits in social networks," Journal of Economic Theory, Elsevier, vol. 154(C), pages 274-309.
    17. Peter Borm & René van den Brink & Marco Slikker, 2002. "An Iterative Procedure for Evaluating Digraph Competitions," Annals of Operations Research, Springer, vol. 109(1), pages 61-75, January.
    18. 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.
    19. Dunia López-Pintado & Duncan J. Watts, 2008. "Social Influence, Binary Decisions and Collective Dynamics," Rationality and Society, , vol. 20(4), pages 399-443, November.
    20. Antoni Calvó-Armengol & Matthew O. Jackson, 2009. "Like Father, Like Son: Social Network Externalities and Parent-Child Correlation in Behavior," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 124-150, February.
    21. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 797-817.
    Full references (including those not matched with items on IDEAS)

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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. 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).
    5. Michel Grabisch & Agnieszka Rusinowska & Xavier Venel, 2022. "Diffusion in large networks," Post-Print halshs-03688783, HAL.
    6. 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.
    7. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining influential models," Post-Print halshs-01318081, HAL.
    8. 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.
    9. 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.
    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. 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.
    12. GRABISCH, Michel & RUSINOWSKA, Agnieszka & VENEL, Xavier, 2022. "Diffusion in large networks," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    13. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Post-Print halshs-02372486, HAL.
    14. repec:hal:pseose:hal-01387480 is not listed on IDEAS
    15. 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.
    16. Merlone, U. & Radi, D., 2014. "Reaching consensus on rumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 260-271.
    17. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02372486, HAL.
    18. 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).
    19. Foerster, Manuel, 2019. "Dynamics of strategic information transmission in social networks," Theoretical Economics, Econometric Society, vol. 14(1), January.
    20. 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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