Abstract

http://ssrn.com/abstract=2627354
 
 

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Surprised by the Gambler's and Hot Hand Fallacies? A Truth in the Law of Small Numbers


Joshua Benjamin Miller


Bocconi University - Department of Decision Sciences; IGIER - Innocenzo Gasparini Institute for Economic Research

Adam Sanjurjo


Universidad de Alicante - Departamento de Fundamentos del Análisis Económico

August 21, 2016

IGIER Working Paper #552

Abstract:     
We find a subtle but substantial bias in a standard measure of the conditional dependence of present outcomes on streaks of past outcomes in sequential data. The mechanism is a form of selection bias, which leads the empirical probability (i.e. relative frequency) to underestimate the true probability of a given outcome, when conditioning on prior outcomes of the same kind. The biased measure has been used prominently in the literature that investigates incorrect beliefs in sequential decision making --- most notably the Gambler's Fallacy and the Hot Hand Fallacy. Upon correcting for the bias, the conclusions of some prominent studies in the literature are reversed. The bias also provides a structural explanation of why the belief in the law of small numbers persists, as repeated experience with finite sequences can only reinforce these beliefs, on average.

Number of Pages in PDF File: 50

Keywords: Law of Small Numbers, Alternation Bias, Negative Recency Bias, Gambler's Fallacy, Hot Hand Fallacy, Hot Hand Effect, Sequential Decision Making, Sequential Data, Selection Bias, Finite Sample Bias, Small Sample Bias

JEL Classification: C12, C14, C18,C19, C91, D03, G02


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Date posted: July 7, 2015 ; Last revised: August 23, 2016

Suggested Citation

Miller, Joshua Benjamin and Sanjurjo, Adam, Surprised by the Gambler's and Hot Hand Fallacies? A Truth in the Law of Small Numbers (August 21, 2016). IGIER Working Paper #552. Available at SSRN: http://ssrn.com/abstract=2627354 or http://dx.doi.org/10.2139/ssrn.2627354

Contact Information

Joshua Benjarmin Miller (Contact Author)
Bocconi University - Department of Decision Sciences ( email )
Via Roentgen 1
Milan, 20136
Italy
HOME PAGE: http://didattica.unibocconi.eu/mypage/index.php?IdUte=111643&lingua=eng
IGIER - Innocenzo Gasparini Institute for Economic Research ( email )
Via Roentgen 1
Milan, 20136
Italy
HOME PAGE: http://didattica.unibocconi.eu/myigier/index.php?IdUte=111643
Adam Sanjurjo
Universidad de Alicante - Departamento de Fundamentos del Análisis Económico ( email )
Campus de San Vicente
Alicante, 03690
Spain
HOME PAGE: http://sites.google.com/site/adamangelsanjurjo/
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