A Bridge from Monty Hall to the Hot Hand: Restricted Choice, Selection Bias, and Empirical Practice

IGIER Working Paper

33 Pages Posted: 2 Jan 2016 Last revised: 29 Oct 2017

Joshua B. Miller

University of Alicante - Department of Economics

Adam Sanjurjo

Universidad de Alicante - Departamento de Fundamentos del Análisis Económico

Date Written: October 27, 2017

Abstract

We show how classic conditional probability puzzles, such as the Monty Hall problem, are intimately related to the hot hand selection bias Miller and Sanjurjo (2015). We explain the connection by way of the principle of restricted choice, an intuitive inferential rule from the card game bridge, which we show is naturally quantified as the updating factor in the odds form of Bayes Rule. We illustrate how, just as the experimental subject fails to use available information to update correctly when choosing a door in the Monty Hall problem, we as researchers can neglect analogous information when designing experiments, analyzing data, and interpreting results.

Keywords: Hot Hand, Hot Hand Fallacy, Monty Hall Problem, Selection Bias, Principle of Restricted Choice, Contract Bridge, Berkson's Paradox, Boy-or-Girl Paradox, Betrand's Box Paradox, Alternation Bias, Gambler's Fallacy, Streak Reversal Paradox, Google Problem, ESP, Psi, Precognition

JEL Classification: C11, C13, C18, C52, C9, D83

Suggested Citation

Miller, Joshua B. and Sanjurjo, Adam, A Bridge from Monty Hall to the Hot Hand: Restricted Choice, Selection Bias, and Empirical Practice (October 27, 2017). IGIER Working Paper. Available at SSRN: https://ssrn.com/abstract=2709837 or http://dx.doi.org/10.2139/ssrn.2709837

Joshua B. Miller (Contact Author)

University of Alicante - Department of Economics ( email )

Apartado de Correos 99
Alicante, 03080
Spain

HOME PAGE: http://joshua-benjamin-miller.com

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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