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Ordered Weighted Averaging in Social Networks

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  • Manuel Förster

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, CORE - Université Catholique de Louvain (UCL) - Belgique)

  • Michel Grabisch

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

  • Agnieszka Rusinowska

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00746988.

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Date of creation: Aug 2012
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Handle: RePEc:hal:cesptp:halshs-00746988

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Keywords: Social network; influence; convergence; speed of convergence; consensus; ordered weighted averaging operator; fuzzy linguistic quantifier.;

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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. 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.
  3. Dunia López-Pintado, 2004. "Diffusion In Complex Social Networks," Working Papers. Serie AD 2004-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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  8. 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.
  9. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
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  11. 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.
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Cited by:
  1. Merlone, U. & Radi, D., 2014. "Reaching consensus on rumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 260-271.
  2. Manuel Förster & Michel Grabisch & Agnieszka Rusinowsk, 2013. "Anonymous Social Influence," Working Papers 2013.51, Fondazione Eni Enrico Mattei.
  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. 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).

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