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A Model of Influence Based on Aggregation Function

  • 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)

The paper concerns a dynamic model of influence in which agents make a yes-no decision. Each agent has an initial opinion which he may change during different phases of interaction, due to mutual influence among agents. We investigate a model of influence based on aggregation functions. Each agent modifies his opinion independently of the others, by aggregating the current opinion of all agents. Our framework covers numerous existing models of opinion formation, since we allow for arbitrary aggregation functions. We provide a general analysis of convergence in the aggregation model and find all terminal classes and states. We show that possible terminal classes to which the process of influence may converge are terminal states (the consensus states and non trivial states), cyclic terminal classes, and unions of Boolean lattices (called regular terminal classes). An agent is influential for another agent if the opinion of the first one matters for the latter. A generalization of influential agent to an irreducible coalition whose opinion matters for an agent is called influential coalition. The graph (hypergraph) of influence is a graphical representation of influential agents (coalitions). Based on properties of the hypergraphs of influence we obtain conditions for the existence of the different kinds of terminal classes. An important family of aggregation functions -- the family of symmetric decomposable models -- is discussed. Finally, based on the results of the paper, we analyze the manager network of Krackhardt.

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Paper provided by HAL in its series PSE - Labex "OSE-Ouvrir la Science Economique" with number halshs-00906367.

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Date of creation: 2013
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Publication status: Published in Mathematical Social Sciences, Elsevier, 2013, pp.316-330
Handle: RePEc:hal:pseose:halshs-00906367
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  1. Michel Grabisch & Agnieszka Rusinowska, 2009. "A model of influence with a continuum of actions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00464460, HAL.
  2. Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344457, HAL.
  3. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
  4. 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.
  5. repec:hal:journl:halshs-00308741 is not listed on IDEAS
  6. Michel Grabisch & Agnieszka Rusinowska, 2010. "Different Approaches to Influence Based on Social Networks and Simple Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00514850, HAL.
  7. 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.
  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.
  9. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 137-156.
  10. Banerjee, Abhijit & Fudenberg, Drew, 2004. "Word-of-mouth learning," Games and Economic Behavior, Elsevier, vol. 46(1), pages 1-22, January.
  11. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2014. "Opinion dynamics and wisdom under conformity," Center for Mathematical Economics Working Papers 469, Center for Mathematical Economics, Bielefeld University.
  12. Ellison, Glenn & Fudenberg, Drew, 1992. "Rules of Thumb for Social Learning," IDEI Working Papers 17, Institut d'Économie Industrielle (IDEI), Toulouse.
  13. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  14. Lorenz, Jan, 2005. "A stabilization theorem for dynamics of continuous opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 217-223.
  15. Glenn Ellison & Drew Fudenberg, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 93-125.
  16. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion bias, social influence, and uni-dimensional opinions," LSE Research Online Documents on Economics 454, London School of Economics and Political Science, LSE Library.
  17. Venkatesh Bala & Sanjeev Goyal, 1998. "Learning from Neighbours," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 595-621.
  18. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 177-209, August.
  19. Dunia López-Pintado, 2004. "Diffusion In Complex Social Networks," Working Papers. Serie AD 2004-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  20. repec:hal:journl:halshs-00583867 is not listed on IDEAS
  21. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445126, HAL.
  22. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 107(3), pages 797-817.
  23. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308741, HAL.
  24. Kirman, Alan P & Oddou, Claude & Weber, Shlomo, 1986. "Stochastic Communication and Coalition Formation," Econometrica, Econometric Society, vol. 54(1), pages 129-38, January.
  25. Pan, Zhengzheng, 2010. "Trust, influence, and convergence of behavior in social networks," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 69-78, July.
  26. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence in command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344805, HAL.
  27. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00355632, HAL.
  28. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
  29. Agnieszka Rusinowska & Michel Grabisch, 2010. "A model of influence with an ordered set of possible actions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00519413, HAL.
  30. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  31. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.
  32. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
  33. 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.
  34. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00344823, HAL.
  35. Bogaçhan Çelen & Shachar Kariv, 2004. "Distinguishing Informational Cascades from Herd Behavior in the Laboratory," American Economic Review, American Economic Association, vol. 94(3), pages 484-498, June.
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