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Naïve Learning in Social Networks: Convergence, Influence and Wisdom of Crowds

  • Matthew O. Jackson

    (Stanford University)

  • Benjamin Golub

    (Division of the Humanities and Social Sciences)

We study learning and influence in a setting where agents communicate according to an arbitrary social network and naïvely update their beliefs by repeatedly taking weighted averages of their neighbors’ opinions. A focus is on conditions under which beliefs of all agents in large societies converge to the truth, despite their naïve updating. We show that this happens if and only if the influence of the most influential agent in the society is vanishing as the society grows. Using simple examples, we identify two main obstructions which can prevent this. By ruling out these obstructions, we provide general structural conditions on the social network that are sufficient for convergence to truth. In addition, we show how social influence changes when some agents redistribute their trust, and we provide a complete characterization of the social networks for which there is a convergence of beliefs. Finally, we survey some recent structural results on the speed of convergence and relate these to issues of segregation, polarization and propaganda.

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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2007.64.

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Date of creation: Jun 2007
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Handle: RePEc:fem:femwpa:2007.64
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  1. 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.
  2. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August.
  3. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
  4. Andrea Galeotti & Sanjeev Goyal, 2007. "A Theory of Strategic Diffusion," Economics Discussion Papers 635, University of Essex, Department of Economics.
  5. Volij, Oscar & Palacios-Huerta, Ignacio, 2004. "The Measurment of Intellectual Influence," Staff General Research Papers 10797, Iowa State University, Department of Economics.
  6. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer, vol. 18(1), pages 39-43, March.
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  8. Shachar Kariv & Syngjoo Choi & Douglas Gale, 2007. "Social Learning in Networks: A Quantal Response Equilibrium Analysis of Experimental Data," Levine's Bibliography 843644000000000107, UCLA Department of Economics.
  9. 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.
  10. Coralio Ballester & Antoni Calvo-Armengol & Yves Zenou, 2005. "Who's Who in Networks. Wanted: the Key Player," NajEcon Working Paper Reviews 666156000000000586, www.najecon.org.
  11. Ellison, Glenn & Fudenberg, Drew, 1992. "Rules of Thumb for Social Learning," IDEI Working Papers 17, Institut d'Économie Industrielle (IDEI), Toulouse.
  12. Ellison, Glenn & Fudenberg, Drew, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, MIT Press, vol. 110(1), pages 93-125, February.
  13. Syngjoo Choi & Douglas Gale & Shachar Kariv, 2005. "Learning in Networks: An Experimental Study," Levine's Bibliography 122247000000000044, UCLA Department of Economics.
  14. Vieille, Nicolas & Rosenberg, Dinah & Solan, Eilon, 2006. "Informational externalities and convergence of behavior," Les Cahiers de Recherche 856, HEC Paris.
  15. Sobel, Joel, 2000. "Economists' Models of Learning," Journal of Economic Theory, Elsevier, vol. 94(2), pages 241-261, October.
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