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A Model of Nonbelief in the Law of Large Numbers

Author

Listed:
  • 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 “nonbelief 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 nonbeliever expects the distribution of signals will have fat tails. In inference, a nonbeliever 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

  • 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.
    • Handle: RePEc:oup:jeurec:v:14:y:2016:i:2:p:515-544.
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    File URL: http://hdl.handle.net/10.1111/jeea.12139
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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. Christopher P. Chambers & Yusufcan Masatlioglu & Collin Raymond, 2023. "Coherent Distorted Beliefs," Papers 2310.09879, arXiv.org, revised Jun 2024.
    7. 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..
    8. Burdin, Gabriel & Landini, Fabio, 2025. "Beliefs and the Demand for Employee Ownership," IZA Discussion Papers 18196, Institute of Labor Economics (IZA).
    9. 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.
    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. He, Xue Dong & Xiao, Di, 2017. "Processing consistency in non-Bayesian inference," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 90-104.
    13. Pedro Bordalo & John J. Conlon & Nicola Gennaioli & Spencer Yongwook Kwon & Andrei Shleifer, 2023. "How People Use Statistics," NBER Working Papers 31631, National Bureau of Economic Research, Inc.
      • 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.
    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. Dzung Bui & Bernd Hayo, 2025. "Inflation Expectations of the General Public under Supply Constraints: Evidence from a Survey Experiment," MAGKS Papers on Economics 202520, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    16. Ilke Aydogan & Aurélien Baillon & Emmanuel Kemel & Chen Li, 2025. "How much do we learn? Measuring symmetric and asymmetric deviations from Bayesian updating through choices," Quantitative Economics, Econometric Society, vol. 16(1), pages 329-365, January.
    17. Farouq Abdulaziz Masoudy, 2018. "Accurate Evaluation of Asset Pricing Under Uncertainty and Ambiguity of Information," Papers 1801.06966, arXiv.org, revised Mar 2018.
    18. George Loewenstein & Zachary Wojtowicz, 2023. "The Economics of Attention," CESifo Working Paper Series 10712, CESifo.
    19. Tomasz Strzalecki, 2024. "Variational Bayes and non-Bayesian Updating," Papers 2405.08796, arXiv.org, revised May 2024.
    20. Jesse Aaron Zinn, 2015. "Expanding the Weighted Updating Model," Economics Bulletin, AccessEcon, vol. 35(1), pages 182-186.
    21. Mauersberger, Felix, 2021. "Monetary policy rules in a non-rational world: A macroeconomic experiment," Journal of Economic Theory, Elsevier, vol. 197(C).
    22. 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).
    23. 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.
    24. Elchin Suleymanov, 2025. "Entropy Regularized Belief Reporting," Papers 2506.22649, arXiv.org, revised Nov 2025.
    25. 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.

    More about this item

    JEL classification:

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

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