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
Universidad de Alicante - Departamento de Fundamentos del Análisis Económico
September 30, 2016
IGIER Working Paper No. 552
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 of a given outcome (i.e. proportion) to underestimate its true probability, when conditioning on prior outcomes of the same kind. The bias has important implications for the literature that investigates incorrect beliefs in sequential decision making --- most notably the Hot Hand Fallacy and the Gambler's Fallacy. When the bias is corrected for, the conclusions of prominent studies in the hot hand fallacy literature are reversed. The bias also provides a structural explanation for how belief in the law of small numbers can persist, even in the face of abundant experience.
Number of Pages in PDF File: 75
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
Date posted: July 7, 2015 ; Last revised: September 30, 2016
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