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Anonymous Social Influence

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  • Manuel Förster

    (Université Paris 1 Panthéon-Sorbonne, France, Université catholique de Louvain – CORE, Belgium)

  • Michel Grabisch

    (Paris School of Economics – Université Paris 1 Panthéon-Sorbonne, France)

  • Agnieszka Rusinowsk

    (Paris School of Economics – CNRS Centre d’Économie de la Sorbonne, 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 extent. 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”.

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Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2013.51.

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Date of creation: May 2013
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Handle: RePEc:fem:femwpa:2013.51

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Keywords: Influence; Anonymity; Ordered Weighted Averaging Operator; Convergence; Consensus; Speed Of Convergence; Fuzzy Linguistic Quantifier;

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References

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  1. Berno Buechel & Tim Hellmann & Stefan Kloessner, 2012. "Opinion Dynamics under Conformity," Working Papers 469, Bielefeld University, Center for Mathematical Economics.
  2. 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.
  3. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  4. Andrea Galeotti & Sanjeev Goyal, 2007. "A Theory of Strategic Diffusion," Economics Discussion Papers 635, University of Essex, Department of Economics.
  5. Manuel Förster & Michel Grabisch & Agnieszka Rusinowsk, 2013. "Anonymous Social Influence," Working Papers 2013.51, Fondazione Eni Enrico Mattei.
  6. Peter M. Demarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, And Unidimensional Opinions," The Quarterly Journal of Economics, MIT Press, vol. 118(3), pages 909-968, August.
  7. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Working Papers 0831, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  8. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
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  17. 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.
  18. Berno Buechel & Tim Hellmann & Michael M. Pichler, 2011. "The Dynamics of Continuous Cultural Traits in Social Networks," Working Papers 457, Bielefeld University, Center for Mathematical Economics.
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  24. 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.
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Citations

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Cited by:
  1. 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).
  2. 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).
  3. PARDO-GARCIA, Christina & SEMPERE-MONERRIS, Jose J., 2013. "Equilibrium mergers in a composite good industry with efficiencies," CORE Discussion Papers 2013067, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Merlone, U. & Radi, D., 2014. "Reaching consensus on rumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 260-271.

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