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A Model of Non-Belief in the Law of Large Numbers

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  • Collin Raymond
  • Daniel J. Benjamin
  • Matthew Rabin

Abstract

People believe that, even in very large samples, proportions of binary signals might depart significantly from the population mean. We model this "non-belief in the Law of Large Numbers" by assuming that a person believes that proportions in any given sample might be determined by a rate different than the true rate. In prediction, a non-believer expects the distribution of signals will have fat tails, more so for larger samples. In inference, a non-believer remains uncertain and influenced by priors even after observing an arbitrarily large sample. We explore implications for beliefs and behavior in a variety of economic settings.

Suggested Citation

  • Collin Raymond & Daniel J. Benjamin & Matthew Rabin, 2013. "A Model of Non-Belief in the Law of Large Numbers," Economics Series Working Papers 672, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:672
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    References listed on IDEAS

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    2. Matthew Rabin, 2002. "Inference by Believers in the Law of Small Numbers," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 775-816.
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    Cited by:

    1. Jawwad Noor & Fernando Payró Chew, 2022. "An Axiomatic Approach to the Law of Small Numbers," Working Papers 1364, Barcelona School of Economics.
    2. Jordan Tong & Daniel Feiler, 2017. "A Behavioral Model of Forecasting: Naive Statistics on Mental Samples," Management Science, INFORMS, vol. 63(11), pages 3609-3627, November.
    3. Crosetto, Paolo & Filippin, Antonio & Katuščák, Peter & Smith, John, 2020. "Central tendency bias in belief elicitation," Journal of Economic Psychology, Elsevier, vol. 78(C).
    4. Hestermann, Nina & Le Yaouanq, Yves, 2018. "It\'s not my Fault! Self-Confidence and Experimentation," Rationality and Competition Discussion Paper Series 124, CRC TRR 190 Rationality and Competition.
    5. Bnaya Dreyfuss & Ori Heffetz & Matthew Rabin, 2019. "Expectations-Based Loss Aversion May Help Explain Seemingly Dominated Choices in Strategy-Proof Mechanisms," NBER Working Papers 26394, National Bureau of Economic Research, Inc.
    6. Jonathan Zinman, 2014. "Consumer Credit: Too Much or Too Little (or Just Right)?," The Journal of Legal Studies, University of Chicago Press, vol. 43(S2), pages 209-237.
    7. Daniel J. Benjamin, 2018. "Errors in Probabilistic Reasoning and Judgment Biases," NBER Working Papers 25200, National Bureau of Economic Research, Inc.
    8. Christopher P. Chambers & Yusufcan Masatlioglu & Collin Raymond, 2023. "Coherent Distorted Beliefs," Papers 2310.09879, arXiv.org, revised Jun 2024.
    9. Scott Duke Kominers & Xiaosheng Mu & Alexander Peysakhovich, 2019. "Paying for Attention: The Impact of Information Processing Costs on Bayesian Inference," Working Papers 2019-31, Princeton University. Economics Department..
    10. Konstantin von Beringe & Mark Whitmeyer, 2024. "The Perils of Overreaction," Papers 2405.08087, arXiv.org.
    11. J. Aislinn Bohren & Daniel N. Hauser, 2023. "Behavioral Foundations of Model Misspecification," PIER Working Paper Archive 23-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    12. Pedro Bordalo & John Conlon & Nicola Gennaioli & Spencer Kwon & Andrei Shleifer, 2023. "How People Use Statistics," Working Papers 699, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    13. He, Xue Dong & Xiao, Di, 2017. "Processing consistency in non-Bayesian inference," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 90-104.
    14. López-Pérez, Raúl & Pintér, Ágnes & Sánchez-Mangas, Rocío, 2022. "Some conditions (not) affecting selection neglect: Evidence from the lab," Journal of Economic Behavior & Organization, Elsevier, vol. 195(C), pages 140-157.
    15. Farouq Abdulaziz Masoudy, 2018. "Accurate Evaluation of Asset Pricing Under Uncertainty and Ambiguity of Information," Papers 1801.06966, arXiv.org, revised Mar 2018.
    16. George Loewenstein & Zachary Wojtowicz, 2023. "The Economics of Attention," CESifo Working Paper Series 10712, CESifo.
    17. Tomasz Strzalecki, 2024. "Variational Bayes and non-Bayesian Updating," Papers 2405.08796, arXiv.org, revised May 2024.
    18. Jesse Aaron Zinn, 2015. "Expanding the Weighted Updating Model," Economics Bulletin, AccessEcon, vol. 35(1), pages 182-186.
    19. Mauersberger, Felix, 2021. "Monetary policy rules in a non-rational world: A macroeconomic experiment," Journal of Economic Theory, Elsevier, vol. 197(C).
    20. López-Pérez, Raúl & Rodriguez-Moral, Antonio & Vorsatz, Marc, 2021. "Simplified mental representations as a cause of overprecision," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 92(C).
    21. Thomas Sproul & Clayton P. Michaud, 2017. "Heterogeneity in loss aversion: evidence from field elicitations," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 77(1), pages 196-216, May.

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    More about this item

    Keywords

    learning; non-Bayesian updating; behavioral economics; information economics;
    All these keywords.

    JEL classification:

    • B49 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Other
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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