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Ordered Weighted Averaging in Social Networks

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 Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 12056.

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Length: 33 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:mse:cesdoc:12056
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  1. Berno Buechel & Tim Hellmann & Stefan Kloessner, 2012. "Opinion Dynamics under Conformity," Center for Mathematical Economics Working Papers 469, Center for Mathematical Economics, Bielefeld University.
  2. Manuel Förster & Michel Grabisch & Agnieszka Rusinowsk, 2013. "Anonymous Social Influence," Working Papers 2013.51, Fondazione Eni Enrico Mattei.
  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. Banerjee, Abhijit & Fudenberg, Drew, 2004. "Word-of-mouth learning," Games and Economic Behavior, Elsevier, vol. 46(1), pages 1-22, January.
  5. repec:hal:journl:halshs-00583867 is not listed on IDEAS
  6. Michel Grabisch & Agnieszka Rusinowska, 2011. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00583867, HAL.
  7. 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.
  8. Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Documents de travail du Centre d'Economie de la Sorbonne b08066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  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. 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.
  11. 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.
  12. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  13. 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.
  14. Sanjeev Goyal & Andrea Galeotti, 2007. "A Theory of Strategic Diffusion," Working Papers 2007.70, Fondazione Eni Enrico Mattei.
  15. 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.
  16. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  17. López-Pintado, Dunia, 2008. "Diffusion in complex social networks," Games and Economic Behavior, Elsevier, vol. 62(2), pages 573-590, March.
  18. repec:hal:journl:halshs-00308741 is not listed on IDEAS
  19. Bala, Venkatesh & Goyal, Sanjeev, 1998. "Learning from Neighbours," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 595-621, July.
  20. repec:hal:journl:halshs-00746988 is not listed on IDEAS
  21. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
  22. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August.
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