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Inference by Believers in the Law of Small Numbers

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Author Info
Matthew Rabin (Economics Department, University of California, Berkeley)
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.

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Paper provided by Department of Economics, Institute for Business and Economic Research, UC Berkeley in its series Department of Economics, Working Paper Series with number 1031.

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Date of creation: 04 Jun 2000
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Handle: RePEc:cdl:econwp:1031

Note: oai:cdlib1:iber/econ-1031
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Related research
Keywords: Bayesian Inference; the gambler's fallacy; law of large numbers; law of small numbers; over-inference;

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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  16. Nicholas Barberis & Ming Huang & Tano Santos, 1999. "Prospect Theory and Asset Prices," NBER Working Papers 7220, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  1. Temple, Jonathan, 2001. "Growing into Trouble: Indonesia After 1966," CEPR Discussion Papers 2932, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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