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

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  • Jackson, Matthew O.
  • Golub, Benjamin

Abstract

We study learning and influence in a setting where agents communicate according to an arbitrary social network and naively 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 naive 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.

Suggested Citation

  • Jackson, Matthew O. & Golub, Benjamin, 2007. "Naive Learning in Social Networks: Convergence, Influence and Wisdom of Crowds," Coalition Theory Network Working Papers 9101, Fondazione Eni Enrico Mattei (FEEM).
    • Handle: RePEc:ags:feemct:9101
    DOI: 10.22004/ag.econ.9101
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    References listed on IDEAS

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    Cited by:

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    2. Itay P. Fainmesser, 2012. "Community Structure and Market Outcomes: A Repeated Games-in-Networks Approach," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 32-69, February.
    3. Michael D. König & S. Battiston & M. Napoletano & F. Schweitzer, 2008. "The Efficiency and Evolution of R&D Networks," CER-ETH Economics working paper series 08/95, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    4. repec:hal:wpspec:info:hdl:2441/9935 is not listed on IDEAS
    5. Daron Acemoglu & Munther A. Dahleh & Ilan Lobel & Asuman Ozdaglar, 2011. "Bayesian Learning in Social Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1201-1236.
    6. Fudenberg, Drew & Takahashi, Satoru, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Games and Economic Behavior, Elsevier, vol. 71(1), pages 100-120, January.
    7. repec:hal:spmain:info:hdl:2441/9933 is not listed on IDEAS
    8. repec:spo:wpmain:info:hdl:2441/9933 is not listed on IDEAS
    9. Paolo Bartesaghi & Michele Benzi & Gian Paolo Clemente & Rosanna Grassi & Ernesto Estrada, 2019. "Risk-dependent centrality in economic and financial networks," Papers 1907.07908, arXiv.org, revised Apr 2020.
    10. repec:hal:wpspec:info:hdl:2441/9933 is not listed on IDEAS
    11. repec:spo:wpecon:info:hdl:2441/9935 is not listed on IDEAS
    12. repec:spo:wpecon:info:hdl:2441/7346 is not listed on IDEAS
    13. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    14. Li-Xin Wang, 2016. "Modeling Stock Price Dynamics with Fuzzy Opinion Networks," Papers 1602.06213, arXiv.org.
    15. Wang, Huanjing & Shang, Lihui, 2015. "Opinion dynamics in networks with common-neighbors-based connections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 180-186.
    16. repec:spo:wpmain:info:hdl:2441/9935 is not listed on IDEAS
    17. Pan, Zhengzheng, 2010. "Trust, influence, and convergence of behavior in social networks," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 69-78, July.
    18. repec:hal:wpspec:info:hdl:2441/7346 is not listed on IDEAS
    19. repec:hal:spmain:info:hdl:2441/9935 is not listed on IDEAS
    20. repec:spo:wpecon:info:hdl:2441/9933 is not listed on IDEAS
    21. repec:spo:wpmain:info:hdl:2441/7346 is not listed on IDEAS
    22. König, Michael D. & Battiston, S. & Napoletano, M. & Schweitzer, F., 2011. "Recombinant knowledge and the evolution of innovation networks," Journal of Economic Behavior & Organization, Elsevier, vol. 79(3), pages 145-164, August.
    23. Zhengzheng Pan & Robert P. Gilles, 2010. "Naive Learning and Game Play in a Dual Social Network Framework," Economics Working Papers 10-01, Queen's Management School, Queen's University Belfast.

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    More about this item

    Keywords

    Institutional and Behavioral Economics;

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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