[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/oup/jeurec/v14y2016i2p515-544..html
   My bibliography  Save this article

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.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/jeea.12139
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. David M. Grether, 1980. "Bayes Rule as a Descriptive Model: The Representativeness Heuristic," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 537-557.
    2. Camerer, Colin F, 1987. "Do Biases in Probability Judgment Matter in Markets? Experimental Evidence," American Economic Review, American Economic Association, vol. 77(5), pages 981-997, December.
    3. 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.
    4. Shunichiro Sasaki & Toshiji Kawagoe, 2007. "Belief Updating in Individual and Social Learning: A Field Experiment on the Internet," ISER Discussion Paper 0690, Institute of Social and Economic Research, Osaka University.
    5. Nelson, Mark W. & Bloomfield, Robert & Hales, Jeffrey W. & Libby, Robert, 2001. "The Effect of Information Strength and Weight on Behavior in Financial Markets," Organizational Behavior and Human Decision Processes, Elsevier, vol. 86(2), pages 168-196, November.
    6. Carlo Kraemer & Martin Weber, 2004. "How Do People Take into Account Weight, Strength and Quality of Segregated vs. Aggregated Data? Experimental Evidence," Journal of Risk and Uncertainty, Springer, vol. 29(2), pages 113-142, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniel J. Benjamin, 2018. "Errors in Probabilistic Reasoning and Judgment Biases," NBER Working Papers 25200, National Bureau of Economic Research, Inc.
    2. He, Xue Dong & Xiao, Di, 2017. "Processing consistency in non-Bayesian inference," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 90-104.
    3. Theo Offerman & Joep Sonnemans, 2004. "What’s Causing Overreaction? An Experimental Investigation of Recency and the Hot‐hand Effect," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 533-554, October.
    4. Nunnari, Salvatore & Zapal, Jan, 2016. "Gambler's fallacy and imperfect best response in legislative bargaining," Games and Economic Behavior, Elsevier, vol. 99(C), pages 275-294.
    5. Dohmen, Thomas & Falk, Armin & Huffman, David & Marklein, Felix & Sunde, Uwe, 2009. "Biased probability judgment: Evidence of incidence and relationship to economic outcomes from a representative sample," Journal of Economic Behavior & Organization, Elsevier, vol. 72(3), pages 903-915, December.
    6. Lex Borghans & Bas ter Weel, 2008. "Understanding the Technology of Computer Technology Diffusion: Explaining Computer Adoption Patterns and Implications for the Wage Structure," Journal of Income Distribution, Ad libros publications inc., vol. 17(3-4), pages 37-70, September.
    7. David M. Frankel, 2008. "Adaptive Expectations And Stock Market Crashes," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(2), pages 595-619, May.
    8. Jason Shachat & Anand Srinivasan, 2022. "Informational Price Cascades and Non-Aggregation of Asymmetric Information in Experimental Asset Markets," Journal of Behavioral Finance, Taylor & Francis Journals, vol. 23(4), pages 388-407, November.
    9. Benjamin Enke & Uri Gneezy & Brian Hall & David Martin & Vadim Nelidov & Theo Offerman & Jeroen van de Ven, 2020. "Cognitive Biases: Mistakes or Missing Stakes?," CESifo Working Paper Series 8168, CESifo.
    10. Feduzi, Alberto & Runde, Jochen, 2014. "Uncovering unknown unknowns: Towards a Baconian approach to management decision-making," Organizational Behavior and Human Decision Processes, Elsevier, vol. 124(2), pages 268-283.
    11. Bruno S. Frey & Reiner Eichenberger, 1989. "Should Social Scientists Care about Choice Anomalies?," Rationality and Society, , vol. 1(1), pages 101-122, July.
    12. He, Kevin, 2022. "Mislearning from censored data: The gambler's fallacy and other correlational mistakes in optimal-stopping problems," Theoretical Economics, Econometric Society, vol. 17(3), July.
    13. Shimon Kogan & Florian H. Schneider & Roberto A. Weber, 2021. "Self-Serving Biases in Beliefs about Collective Outcomes," CESifo Working Paper Series 8975, CESifo.
    14. David Hirshleifer, 2001. "Investor Psychology and Asset Pricing," Journal of Finance, American Finance Association, vol. 56(4), pages 1533-1597, August.
    15. Ambuehl, Sandro & Li, Shengwu, 2018. "Belief updating and the demand for information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 21-39.
    16. Rabin, Matthew, 2000. "Inference by Believers in the Law of Small Numbers," Department of Economics, Working Paper Series qt4sw8n41t, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    17. 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.
    18. Antoniou, Constantinos & Harrison, Glenn W. & Lau, Morten I. & Read, Daniel, 2017. "Information Characteristics and Errors in Expectations: Experimental Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(2), pages 737-750, April.
    19. Alós-Ferrer, Carlos & Hügelschäfer, Sabine, 2012. "Faith in intuition and behavioral biases," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 182-192.
    20. Alós-Ferrer, Carlos & Mihm, Maximilian, 2023. "An Axiomatic Characterization of Bayesian Updating," Journal of Mathematical Economics, Elsevier, vol. 104(C).

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:jeurec:v:14:y:2016:i:2:p:515-544.. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/jeea .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.