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A Model Of Nonbelief In The Law Of Large Numbers

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  • Daniel J. Benjamin
  • Matthew Rabin
  • Collin Raymond

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.
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Suggested Citation

  • Daniel J. Benjamin & Matthew Rabin & Collin Raymond, 2016. "A Model Of Nonbelief In The Law Of Large Numbers," Journal of the European Economic Association, European Economic Association, vol. 14(2), pages 515-544, April.
    • Handle: RePEc:bla:jeurec:v:14:y:2016:i:2:p:515-544
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    File URL: http://hdl.handle.net/10.1111/jeea.2016.14.issue-2
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    Cited by:

    1. Crosetto, Paolo & Filippin, Antonio & Katuščák, Peter & Smith, John, 2020. "Central tendency bias in belief elicitation," Journal of Economic Psychology, Elsevier, vol. 78(C).
    2. Daniel J. Benjamin, 2018. "Errors in Probabilistic Reasoning and Judgment Biases," GRU Working Paper Series GRU_2018_023, City University of Hong Kong, Department of Economics and Finance, Global Research Unit.
    3. Jawwad Noor & Fernando Payró Chew, 2022. "An Axiomatic Approach to the Law of Small Numbers," Working Papers 1364, Barcelona School of Economics.
    4. 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.
    5. Konstantin von Beringe & Mark Whitmeyer, 2024. "The Perils of Overreaction," Papers 2405.08087, arXiv.org.
    6. 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.
    7. 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.
    8. 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.
    9. He, Xue Dong & Xiao, Di, 2017. "Processing consistency in non-Bayesian inference," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 90-104.
    10. 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.
    11. 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.
    12. Farouq Abdulaziz Masoudy, 2018. "Accurate Evaluation of Asset Pricing Under Uncertainty and Ambiguity of Information," Papers 1801.06966, arXiv.org, revised Mar 2018.
    13. 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.
    14. George Loewenstein & Zachary Wojtowicz, 2023. "The Economics of Attention," CESifo Working Paper Series 10712, CESifo.
    15. Tomasz Strzalecki, 2024. "Variational Bayes and non-Bayesian Updating," Papers 2405.08796, arXiv.org, revised May 2024.
    16. Jesse Aaron Zinn, 2015. "Expanding the Weighted Updating Model," Economics Bulletin, AccessEcon, vol. 35(1), pages 182-186.
    17. Mauersberger, Felix, 2021. "Monetary policy rules in a non-rational world: A macroeconomic experiment," Journal of Economic Theory, Elsevier, vol. 197(C).
    18. Christopher P. Chambers & Yusufcan Masatlioglu & Collin Raymond, 2023. "Coherent Distorted Beliefs," Papers 2310.09879, arXiv.org, revised Jun 2024.
    19. 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..
    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

    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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