IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/23927.html
   My bibliography  Save this paper

Biased Beliefs About Random Samples: Evidence from Two Integrated Experiments

Author

Listed:
  • Daniel J. Benjamin
  • Don A. Moore
  • Matthew Rabin

Abstract

This paper describes results of a pair of incentivized experiments on biases in judgments about random samples. Consistent with the Law of Small Numbers (LSN), participants exaggerated the likelihood that short sequences and random subsets of coin flips would be balanced between heads and tails. Consistent with the Non-Belief in the Law of Large Numbers (NBLLN), participants underestimated the likelihood that large samples would be close to 50% heads. However, we identify some shortcomings of existing models of LSN, and we find that NBLLN may not be as stable as previous studies suggest. We also find evidence for exact representativeness (ER), whereby people tend to exaggerate the likelihood that samples will (nearly) exactly mirror the underlying odds, as an additional bias beyond LSN. Our within-subject design of asking many different questions about the same data lets us disentangle the biases from possible rational alternative interpretations by showing that the biases lead to inconsistency in answers. Our design also centers on identifying and controlling for bin effects, whereby the probability assigned to outcomes systematically depends on the categories used to elicit beliefs in a way predicted by support theory. The bin effects are large and systematic and affect some results, but we find LSN, NBLLN, and ER even after controlling for them.

Suggested Citation

  • Daniel J. Benjamin & Don A. Moore & Matthew Rabin, 2017. "Biased Beliefs About Random Samples: Evidence from Two Integrated Experiments," NBER Working Papers 23927, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:23927
    Note: AG
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w23927.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Matthew Rabin & Dimitri Vayanos, 2010. "The Gambler's and Hot-Hand Fallacies: Theory and Applications," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 730-778.
    2. Joshua B. Miller & Adam Sanjurjo, 2015. "Surprised by the Gambler’s and Hot Hand Fallacies? A Truth in the Law of Small Numbers," Working Papers 552, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. Rachel Croson & James Sundali, 2005. "The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos," Journal of Risk and Uncertainty, Springer, vol. 30(3), pages 195-209, May.
    4. Jeff Dominitz & Charles F. Manski, 2007. "Expected Equity Returns and Portfolio Choice: Evidence from the Health and Retirement Study," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 369-379, 04-05.
    5. Craig R. Fox & Robert T. Clemen, 2005. "Subjective Probability Assessment in Decision Analysis: Partition Dependence and Bias Toward the Ignorance Prior," Management Science, INFORMS, vol. 51(9), pages 1417-1432, September.
    6. Sigrid Suetens & Claus B. Galbo-Jørgensen & Jean-Robert Tyran, 2016. "Predicting Lotto Numbers: A Natural Experiment On The Gambler'S Fallacy And The Hot-Hand Fallacy," Journal of the European Economic Association, European Economic Association, vol. 14(3), pages 584-607, June.
    7. Terrell, Dek, 1994. "A Test of the Gambler's Fallacy: Evidence from Pari-mutuel Games," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 309-317, May.
    8. Matthew Rabin, 2002. "Inference by Believers in the Law of Small Numbers," The Quarterly Journal of Economics, Oxford University Press, vol. 117(3), pages 775-816.
    9. Daniel M. Oppenheimer & Benoit Monin, 2009. "The retrospective gambler's fallacy: Unlikely events, constructing the past, and multiple universes," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 4(5), pages 326-334, August.
    10. Uriel Haran & Don A. Moore & Carey K. Morewedge, 2010. "A simple remedy for overprecision in judgment," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 5(7), pages 467-476, December.
    11. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    12. Chen, Daniel L. & Moskowitz, Tobias J. & Shue, Kelly, 2016. "Decision-Making Under the Gambler’s Fallacy: Evidence From Asylum Courts, Loan Officers, and Baseball Umpires," IAST Working Papers 16-43, Institute for Advanced Study in Toulouse (IAST).
    13. repec:oup:jeurec:v:14:y:2016:i:3:p:584-607. is not listed on IDEAS
    14. repec:hrv:faseco:30747159 is not listed on IDEAS
    15. Viscusi, W Kip, 1990. "Do Smokers Underestimate Risks?," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1253-1269, December.
    16. Daniel L. Chen & Tobias J. Moskowitz & Kelly Shue, 2016. "Decision Making Under the Gambler’s Fallacy: Evidence from Asylum Judges, Loan Officers, and Baseball Umpires," The Quarterly Journal of Economics, Oxford University Press, vol. 131(3), pages 1181-1242.
    Full references (including those not matched with items on IDEAS)

    More about this item

    JEL classification:

    • B49 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Other
    • D99 - Microeconomics - - Micro-Based Behavioral Economics - - - Other

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:nbr:nberwo:23927. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://edirc.repec.org/data/nberrus.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.