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Anonymous social influence

  • 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)

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 fewâ€.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2013028.

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Date of creation: 04 Jul 2013
Date of revision:
Handle: RePEc:cor:louvco:2013028
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  1. Manuel Foerster & Michel Grabisch & Agnieszka Rusinowska, 2013. "Anonymous social influence," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00913235, HAL.
  2. 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.
  3. Michel Grabisch & Agnieszka Rusinowska, 2011. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00583867, HAL.
  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. Michel Grabisch & Agnieszka Rusinowska, 2011. "A model of influence based on aggregation functions," Documents de travail du Centre d'Economie de la Sorbonne 11058, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  6. Borm, P.E.M. & van den Brink, J.R. & Slikker, M., 2002. "An iterative procedure for evaluating digraph competitions," Other publications TiSEM 40ae2ec2-efdb-48f6-905c-5, Tilburg University, School of Economics and Management.
  7. Dunia López-Pintado, 2004. "Diffusion In Complex Social Networks," Working Papers. Serie AD 2004-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. repec:bla:restud:v:65:y:1998:i:3:p:595-621 is not listed on IDEAS
  9. Banerjee, Abhijit & Fudenberg, Drew, 2004. "Word-of-mouth learning," Games and Economic Behavior, Elsevier, vol. 46(1), pages 1-22, January.
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  11. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, and Unidimensional Opinions," The Quarterly Journal of Economics, Oxford University Press, vol. 118(3), pages 909-968.
  12. 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, 06.
  13. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  14. 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.
  15. Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344457, HAL.
  16. repec:hal:journl:halshs-00583867 is not listed on IDEAS
  17. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
  18. Bala, V. & Goyal, S., 1995. "Learning from Neighbors," Econometric Institute Research Papers EI 9549-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  19. Sanjeev Goyal & Andrea Galeotti, 2007. "A Theory of Strategic Diffusion," Working Papers 2007.70, Fondazione Eni Enrico Mattei.
  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 124-50, February.
  21. repec:hal:journl:halshs-00746988 is not listed on IDEAS
  22. 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.
  23. repec:hal:journl:halshs-00308741 is not listed on IDEAS
  24. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
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