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Inference by Believers in the Law of Small Numbers

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  • Rabin, Matthew

Abstract

Many people believe in the "Law of Small Numbers," exaggerating the degree to which a small sample resembles the population from which it is drawn. To model this, I assume that a person exaggerates the likelihood that a short sequence of i.i.d. signals resembles the long-run rate at which those signals are generated. Such a person believes in the "gambler's fallacy", thinking early draws of one signal increase the odds of next drawing other signals. When uncertain about the rate, the person over-infers from short sequences of signals, and is prone to think the rate is more extreme than it is. When the person makes inferences about the frequency at which rates are generated by different sources -- such as the distribution of talent among financial analysts -- based on few observations from each source, he tends to exaggerate how much variance there is in the rates. Hence, the model predicts that people may pay for financial advice from "experts" whose expertise is entirely illusory. Other economic applications are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:cdl:econwp:qt4sw8n41t
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    Cited by:

    1. Berg, Nathan, 2003. "Normative behavioral economics," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 32(4), pages 411-427, September.
    2. David Hirshleifer, 2001. "Investor Psychology and Asset Pricing," Journal of Finance, American Finance Association, vol. 56(4), pages 1533-1597, August.
    3. Chan, Wesley & Frankel, Richard & Kothari, S.P., 2002. "Testing Behavioral Finance Theories Using Trends and Sequences in Financial Performance," Working papers 4375-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Shun-Chuan Chang, 2018. "Capability and opportunity in hot shooting performance: Evidence from top-scoring NBA leaders," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-14, February.
    5. Tirole, Jean, 2002. "Rational irrationality: Some economics of self-management," European Economic Review, Elsevier, vol. 46(4-5), pages 633-655, May.
    6. Kahn Matthew E., 2015. "Climate Change Adaptation Will Offer a Sharp Test of the Claims of Behavioral Economics," The Economists' Voice, De Gruyter, vol. 12(1), pages 25-30, August.
    7. Temple, Jonathan, 2001. "Growing into Trouble: Indonesia After 1966," CEPR Discussion Papers 2932, C.E.P.R. Discussion Papers.
    8. Baquero, G. & Verbeek, M.J.C.M., 2006. "Do Sophisticated Investors Believe in the Law of Small Numbers?," ERIM Report Series Research in Management ERS-2006-033-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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    More about this item

    Keywords

    Bayesian Inference; the gambler's fallacy; law of large numbers; law of small numbers; over-inference;
    All these keywords.

    JEL classification:

    • B49 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Other

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