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Inference by Believers in the Law of Small Numbers

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  • Matthew Rabin.

Abstract

JEL#: B49 Keywords: Bayesian Inference, the gambler' fallacy, law of large numbers, law of small numbers, over-inference 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. June 2000

Suggested Citation

  • Matthew Rabin., 2000. "Inference by Believers in the Law of Small Numbers," Economics Working Papers E00-282, University of California at Berkeley.
  • Handle: RePEc:ucb:calbwp:e00-282
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    References listed on IDEAS

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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. 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.
    3. Tirole, Jean, 2002. "Rational irrationality: Some economics of self-management," European Economic Review, Elsevier, vol. 46(4-5), pages 633-655, May.
    4. Temple, Jonathan, 2001. "Growing into Trouble: Indonesia After 1966," CEPR Discussion Papers 2932, C.E.P.R. Discussion Papers.

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    JEL classification:

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

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