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Ordered Weighted Averaging in Social Networks

  • 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)

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
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00746988
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  1. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
  2. repec:ner:tilbur:urn:nbn:nl:ui:12-90188 is not listed on IDEAS
  3. 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.
  4. 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.
  5. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  6. Berno Buechel & Tim Hellmann & Stefan Kloessner, 2012. "Opinion Dynamics under Conformity," Working Papers 469, Bielefeld University, Center for Mathematical Economics.
  7. 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.
  8. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  9. 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.
  10. Abhijit Banerjee & Drew Fudenberg, 2010. "Word of Mouth Learning," Levine's Working Paper Archive 723, David K. Levine.
  11. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August.
  12. López-Pintado, Dunia, 2008. "Diffusion in complex social networks," Games and Economic Behavior, Elsevier, vol. 62(2), pages 573-590, March.
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