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The Wisdom of the Crowd and Higher-Order Beliefs

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  • Yi-Chun Chen
  • Manuel Mueller-Frank
  • Mallesh M Pai

Abstract

The classic wisdom-of-the-crowd problem asks how a principal can "aggregate" information about the unknown state of the world from agents without understanding the information structure among them. We propose a new simple procedure called Population-Mean-Based Aggregation to achieve this goal. The procedure only requires eliciting agents' beliefs about the state, and also eliciting some agents' expectations of the average belief in the population. We show that this procedure fully aggregates information: in an infinite population, it always infers the true state of the world. The procedure can accommodate correlations in agents' information, misspecified beliefs, any finite number of possible states of the world, and only requires very weak assumptions on the information structure.

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  • Yi-Chun Chen & Manuel Mueller-Frank & Mallesh M Pai, 2021. "The Wisdom of the Crowd and Higher-Order Beliefs," Papers 2102.02666, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2102.02666
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    References listed on IDEAS

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    1. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections with Private Information," Econometrica, Econometric Society, vol. 65(5), pages 1029-1058, September.
    2. Marco Ottaviani & Peter Norman Sørensen, 2015. "Price Reaction to Information with Heterogeneous Beliefs and Wealth Effects: Underreaction, Momentum, and Reversal," American Economic Review, American Economic Association, vol. 105(1), pages 1-34, January.
    3. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    4. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    5. Justin Wolfers & Eric Zitzewitz, 2004. "Prediction Markets," Journal of Economic Perspectives, American Economic Association, vol. 18(2), pages 107-126, Spring.
    6. Edi Karni, 2009. "A Mechanism for Eliciting Probabilities," Econometrica, Econometric Society, vol. 77(2), pages 603-606, March.
    7. Dražen Prelec & H. Sebastian Seung & John McCoy, 2017. "A solution to the single-question crowd wisdom problem," Nature, Nature, vol. 541(7638), pages 532-535, January.
    8. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Barton L. Lipman, 2003. "Finite Order Implications of Common Priors," Econometrica, Econometric Society, vol. 71(4), pages 1255-1267, July.
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    Cited by:

    1. Dirk Bergemann & Marco Ottaviani, 2021. "Information Markets and Nonmarkets," Cowles Foundation Discussion Papers 2296, Cowles Foundation for Research in Economics, Yale University.

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