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Anonymous social influence

  • Manuel Foerster

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain)

  • Michel Grabisch


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

  • Agnieszka Rusinowska


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

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 modeled 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 averages are only used to some extent. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like "most" or "at least a few".

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Paper provided by HAL in its series PSE - Labex "OSE-Ouvrir la Science Economique" with number halshs-00913235.

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Date of creation: 2013
Date of revision:
Publication status: Published in Games and Economic Behavior, Elsevier, 2013, pp.621-635
Handle: RePEc:hal:pseose:halshs-00913235
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  1. Abhijit Banerjee & Drew Fudenberg, 2010. "Word of Mouth Learning," Levine's Working Paper Archive 723, David K. Levine.
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  3. Michel Grabisch & Agnieszka Rusinowska, 2013. "A Model of Influence Based on Aggregation Function," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00906367, HAL.
  4. FÖRSTER, Manuel & GRABISCH, Michel & RUSINOWSKA, Agnieszka, 2013. "Anonymous social influence," CORE Discussion Papers 2013028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  9. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  10. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00355632, HAL.
  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.
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  13. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
  14. Berno Buechel & Tim Hellmann & Michael M. Pichler, 2011. "The Dynamics of Continuous Cultural Traits in Social Networks," Center for Mathematical Economics Working Papers 457, Center for Mathematical Economics, Bielefeld University.
  15. Büchel, Berno & Hellmann, Tim & Klößner, Stefan, 2013. "Opinion Dynamics and Wisdom under Conformity," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79770, Verein für Socialpolitik / German Economic Association.
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