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

We show how classic conditional probability puzzles, such as the Monty Hall problem, are intimately related to the recently discovered hot hand selection bias. 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’s 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, researchers may neglect analogous information when designing experiments, analyzing data, and interpreting results.

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

10.31219/osf.io/dmgtp ◽

2018 ◽

Cited By ~ 2

Author(s):

Joshua Benjamin Miller ◽

Adam Sanjurjo

Keyword(s):

Conditional Probability ◽

Selection Bias ◽

Experimental Subject ◽

Bayes Rule ◽

Card Game ◽

Hot Hand ◽

Monty Hall ◽

Monty Hall Problem ◽

Available Information ◽

Inferential Rule

We show how classic conditional probability puzzles, such as the Monty Hall problem, are intimately related to the hot hand selection bias. 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, researchers may neglect analogous information when designing experiments, analyzing data, and interpreting results.

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Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers

10.31219/osf.io/sv9x2 ◽

2018 ◽

Author(s):

Joshua Benjamin Miller ◽

Adam Sanjurjo

Keyword(s):

Selection Bias ◽

Empirical Work ◽

Sequential Data ◽

Bibliographic Reference ◽

Conditional Dependence ◽

Hot Hand ◽

The Law ◽

Substantial Bias

*Econometrica Link*: https://www.econometricsociety.org/publications/econometrica/2018/11/01/surprised-hot-hand-fallacy-truth-law-small-numbers *Full Bibliographic Reference*: Miller, J. B., & Sanjurjo, A. (2018). Surprised by the hot hand fallacy? A truth in the law of small numbers. Econometrica, Vol. 86, No.6, pp. 2019–2047 ********************************************* We prove that a subtle but substantial bias exists in a common measure of the conditional dependence of present outcomes on streaks of past outcomes in sequential data. The magnitude of this streak selection bias generally decreases as the sequence gets longer, but increases in streak length, and remains substantial for a range of sequence lengths often used in empirical work. We observe that the canonical study in the influential hot hand fallacy literature, along with replications, are vulnerable to the bias. Upon correcting for the bias we find that the long-standing conclusions of the canonical study are reversed.

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Working Memory Capacity and a Notorious Brain Teaser

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169.53.1.123 ◽

2006 ◽

Vol 53 (2) ◽

pp. 123-131 ◽

Cited By ~ 29

Author(s):

Wim De Neys ◽

Niki Verschueren

Keyword(s):

Working Memory ◽

Secondary Task ◽

Working Memory Capacity ◽

Memory Capacity ◽

Task Load ◽

Normative Reasoning ◽

Monty Hall Dilemma ◽

Monty Hall ◽

Memory Resources

Abstract. The Monty Hall Dilemma (MHD) is an intriguing example of the discrepancy between people’s intuitions and normative reasoning. This study examines whether the notorious difficulty of the MHD is associated with limitations in working memory resources. Experiment 1 and 2 examined the link between MHD reasoning and working memory capacity. Experiment 3 tested the role of working memory experimentally by burdening the executive resources with a secondary task. Results showed that participants who solved the MHD correctly had a significantly higher working memory capacity than erroneous responders. Correct responding also decreased under secondary task load. Findings indicate that working memory capacity plays a key role in overcoming salient intuitions and selecting the correct switching response during MHD reasoning.

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