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

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  • Matthew O. Jackson

    (Stanford University)

  • Benjamin Golub

    (Division of the Humanities and Social Sciences)

Abstract

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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Bibliographic Info

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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Keywords: Social Networks; Learning; Diffusion; Bounded Rationality;

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  1. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Syngjoo Choi & Douglas Gale & Shachar Kariv, 2012. "Social learning in networks: a Quantal Response Equilibrium analysis of experimental data," Review of Economic Design, Springer, vol. 16(2), pages 135-157, September.
  3. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer, vol. 18(1), pages 39-43, March.
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  7. Andrea Galeotti & Sanjeev Goyal, 2007. "A Theory of Strategic Diffusion," Economics Discussion Papers 635, University of Essex, Department of Economics.
  8. Volij, Oscar & Palacios-Huerta, Ignacio, 2004. "The Measurment of Intellectual Influence," Staff General Research Papers 10797, Iowa State University, Department of Economics.
  9. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August.
  10. Banerjee, Abhijit & Fudenberg, Drew, 2004. "Word-of-mouth learning," Games and Economic Behavior, Elsevier, vol. 46(1), pages 1-22, January.
  11. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
  12. Sobel, Joel, 2000. "Economists' Models of Learning," Journal of Economic Theory, Elsevier, vol. 94(2), pages 241-261, October.
  13. Syngjoo Choi & Douglas Gale & Shachar Kariv, 2005. "Learning in Networks: An Experimental Study," Levine's Bibliography 122247000000000044, UCLA Department of Economics.
  14. 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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