Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00746988.html
   My bibliography  Save this paper

Ordered Weighted Averaging in Social Networks

Author

Listed:
  • Manuel Förster

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UCL - Université Catholique de Louvain = Catholic University of Louvain)

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Agnieszka Rusinowska

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

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://shs.hal.science/halshs-00746988
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00746988/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Venkatesh Bala & Sanjeev Goyal, 1998. "Learning from Neighbours," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 595-621.
    2. Banerjee, Abhijit & Fudenberg, Drew, 2004. "Word-of-mouth learning," Games and Economic Behavior, Elsevier, vol. 46(1), pages 1-22, January.
    3. 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.
    4. Goyal, Sanjeev & Galeotti, Andrea, 2007. "A Theory of Strategic Diffusion," Coalition Theory Network Working Papers 9096, Fondazione Eni Enrico Mattei (FEEM).
    5. 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.
    6. 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.
    7. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
    8. 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.
    9. 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.
    10. López-Pintado, Dunia, 2008. "Diffusion in complex social networks," Games and Economic Behavior, Elsevier, vol. 62(2), pages 573-590, March.
    11. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    12. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
    13. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining influential models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01318081, HAL.
    5. 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.
    6. 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.
    7. 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.
    8. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02372486, HAL.
    9. 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.
    10. GRABISCH, Michel & RUSINOWSKA, Agnieszka & VENEL, Xavier, 2022. "Diffusion in large networks," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    11. Foerster, Manuel, 2019. "Dynamics of strategic information transmission in social networks," Theoretical Economics, Econometric Society, vol. 14(1), January.
    12. Michel Grabisch & Agnieszka Rusinowska & Xavier Venel, 2022. "Diffusion in large networks," Post-Print halshs-03688783, HAL.
    13. 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.
    14. Poindron, Alexis, 2021. "A general model of binary opinions updating," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 52-76.
    15. Merlone, U. & Radi, D., 2014. "Reaching consensus on rumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 260-271.
    16. 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.
    17. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Post-Print halshs-02372486, HAL.
    18. repec:hal:pseose:hal-01387480 is not listed on IDEAS
    19. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    2. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    3. repec:hal:pseose:halshs-00906367 is not listed on IDEAS
    4. 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.
    5. 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.
    6. Michel Grabisch & Agnieszka Rusinowska, 2020. "A Survey on Nonstrategic Models of Opinion Dynamics," Games, MDPI, vol. 11(4), pages 1-29, December.
    7. Matthew O. Jackson & Benjamin Golub, 2007. "Naïve Learning in Social Networks: Convergence, Influence and Wisdom of Crowds," Working Papers 2007.64, Fondazione Eni Enrico Mattei.
    8. 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.
    9. 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.
    10. Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska & Emily Tanimura, 2018. "Strategic Influence in Social Networks," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 29-50, February.
    11. repec:hal:pseose:hal-01387480 is not listed on IDEAS
    12. Prummer, Anja & Siedlarek, Jan-Peter, 2014. "Institutions And The Preservation Of Cultural Traits," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 470, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    13. Jadbabaie, Ali & Molavi, Pooya & Sandroni, Alvaro & Tahbaz-Salehi, Alireza, 2012. "Non-Bayesian social learning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 210-225.
    14. Daron Acemoglu & Asuman Ozdaglar, 2011. "Opinion Dynamics and Learning in Social Networks," Dynamic Games and Applications, Springer, vol. 1(1), pages 3-49, March.
    15. Daron Acemoglu & Munther A. Dahleh & Ilan Lobel & Asuman Ozdaglar, 2011. "Bayesian Learning in Social Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1201-1236.
    16. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining influential models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01318081, HAL.
    17. Ilan Lobel & Evan Sadler, 2016. "Preferences, Homophily, and Social Learning," Operations Research, INFORMS, vol. 64(3), pages 564-584, June.
    18. Battiston, Pietro & Stanca, Luca, 2015. "Boundedly rational opinion dynamics in social networks: Does indegree matter?," Journal of Economic Behavior & Organization, Elsevier, vol. 119(C), pages 400-421.
    19. Camargo, Braz, 2014. "Learning in society," Games and Economic Behavior, Elsevier, vol. 87(C), pages 381-396.
    20. James C. D. Fisher & John Wooders, 2017. "Interacting information cascades: on the movement of conventions between groups," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 211-231, January.
    21. Tsakas, Nikolas, 2012. "Naive learning in social networks: Imitating the most successful neighbor," MPRA Paper 37796, University Library of Munich, Germany.
    22. Mark Bowden & Stuart McDonald, 2008. "The Impact of Interaction and Social Learning on Aggregate Expectations," Computational Economics, Springer;Society for Computational Economics, vol. 31(3), pages 289-306, April.

    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;
    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00746988. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.