Why Humans Fail in Solving the Monty Hall Dilemma: A Systematic Review

Saenen, Lore; Heyvaert, Mieke; Dooren, Wim Van; Schaeken, Walter; Onghena, Patrick

doi:10.5334/pb.274

Cited by 11 publications

(8 citation statements)

References 44 publications

(261 reference statements)

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“…Furthermore, Saenen et al (2018) state that improving understanding in the Monty Hall problem is an unresolved challenge; however, the experiments reported in this article indicate that perhaps this challenge is resolvable. Across both experiments, 22 participants in total gave correct posterior probabilities and reported using-or being affected by-the mental simulations approach.…”

Section: Improving Understanding Of the Monty Hall Problemsmentioning

confidence: 88%

“…Instead, erroneous responses are explained primarily in other terms, including 1) emotional-based choice biases where participants are averse to switching from their first choice (Granberg & Dorr, 1998), and 2) various other cognitive limitations in understanding and representing probabilities involved in why participants think the two outcomes are equally probable given the evidence (De Neys & Verschueren, 2006;Tubau et al, 2003). A comprehensive description of all competing theories is impossible here, but see Saenen et al (2018) and Tubau et al (2015) for some comprehensive reviews of the existing literature. This study investigates the hypothesis that likelihood neglect exists and partially explains erroneous responses to the Monty Hall problem.…”

Section: Introduction 11 Likelihoods Likelihood Neglect Bias and The ...mentioning

confidence: 99%

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Likelihood Neglect Bias and the Mental Simulations Approach: An Illustration using the Old and New Monty Hall Problems

Wilcox

2024

Preprint

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This article introduces a new violation of a law probability, likelihood neglect bias. The bias occurs when one is (i) aware that some evidence is more likely given one hypothesis rather than another, but (ii) that evidence does not cause them to raise their probability for the former hypothesis relative to the latter. The Monty Hall problem illustrates this bias, although the bias is potentially present in other contexts. Unlike previous studies, the present study shows that incorrect responses to the problem are attributable to failure to realize the implications of likelihoods (i.e. likelihood neglect) instead of unawareness of what the likelihoods are. Likelihood neglect is also distinguished from other biases which it is occasionally confused with, and a theoretical explanation of likelihood neglect is proposed. Experimental results also indicate that a new approach—the mental simulations approach—showed a large effect in reducing likelihood neglect and increasing correct probabilities when encountering the Monty Hall problem. The approach also increased correct probabilities for a new modification called the “New Monty Hall problem”, unlike two prominent alternative approaches to the original Monty Hall problem.

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Section: Improving Understanding Of the Monty Hall Problemsmentioning

confidence: 88%

Section: Introduction 11 Likelihoods Likelihood Neglect Bias and The ...mentioning

confidence: 99%

Likelihood Neglect Bias and the Mental Simulations Approach: An Illustration using the Old and New Monty Hall Problems

Wilcox

2024

Preprint

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“…Remarkably, even when people are shown explanations, simulations and mathematical proofs, many - including renown statisticians - still refuse to accept the answer of the puzzle [58, 59]. Studies using repeated simulations of the Monte Hall problem show a remarkable adoption of the correct answer.…”

Section: Discussionmentioning

confidence: 99%

Published benefits of ivermectin use in Itajaí, Brazil for COVID-19 infection, hospitalisation, and mortality are entirely explained by statistical artefacts

Mills¹,

Antônio

Tucker‐Kellogg

2023

Preprint

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BackgroundTwo recent publications by Kerr et al. (Cureus 14(1):e21272; Cureus 14(8): e28624) reported dramatic effects of prophylactic ivermectin use for both prevention of COVID-19 and reduction of COVID-19-related hospitalisation and mortality, including a dose-dependent effect of ivermectin prophylaxis. These papers have gained an unusually large public influence: they were incorporated into debates around COVID-19 policies and may have contributed to decreased trust in vaccine efficacy and public health authorities more broadly. Both studies were based on retrospective observational analysis of city-wide registry data from the city of Itajaí, Brazil from July-December 2020.MethodsStarting with initially identified sources of error, we conducted a revised statistical analysis of available data, including data made available with the original papers and public data from the Brazil Ministry of Health. We identified additional uncorrected sources of bias and errors from the original analysis, including incorrect subject exclusion and missing subjects, an enrolment time bias, and multiple sources of immortal time bias. In models assuming no actual effect from ivermectin use, we conducted Monte Carlo simulations to estimate the contribution of these biases to any observed effect.ResultsUntreated statistical artefacts and methodological errors alone lead to dramatic apparent risk reduction associated with ivermectin use in both studies. The magnitude of apparent risk reduction from these artefacts is comparable to the results reported by the studies themselves, including apparent protection from infection, hospitalisation, and death, and including the reported apparent dose-response relationship.ConclusionsThe inference of ivermectin efficacy reported in both papers is unsupported, as the observed effects are entirely explained by untreated statistical artefacts and methodological errors. Our re-analysis calls for caution in interpreting highly publicised observational studies and highlights the importance of common sources of bias in clinical research.

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“…For instance, Krauss and Wang (2003) added a frequency question in order to exploit the natural frequency concept, and subsequently Krauss and Atmaca (2004) made the option of a frequency algorithm even more salient by clearly depicting the three possible car-goat constellations (see Figure 1, right). For a recent review of literature addressing why humans systematically fail to react optimally to the Monty Hall problem, see Saenen et al (2018).…”

Section: Reads As Followsmentioning

confidence: 99%

Tversky and Kahneman’s Cognitive Illusions: Who Can Solve Them, and Why?

et al. 2021

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In the present paper we empirically investigate the psychometric properties of some of the most famous statistical and logical cognitive illusions from the “heuristics and biases” research program by Daniel Kahneman and Amos Tversky, who nearly 50 years ago introduced fascinating brain teasers such as the famous Linda problem, the Wason card selection task, and so-called Bayesian reasoning problems (e.g., the mammography task). In the meantime, a great number of articles has been published that empirically examine single cognitive illusions, theoretically explaining people’s faulty thinking, or proposing and experimentally implementing measures to foster insight and to make these problems accessible to the human mind. Yet these problems have thus far usually been empirically analyzed on an individual-item level only (e.g., by experimentally comparing participants’ performance on various versions of one of these problems). In this paper, by contrast, we examine these illusions as a group and look at the ability to solve them as a psychological construct. Based on an sample of N = 2,643 Luxembourgian school students of age 16–18 we investigate the internal psychometric structure of these illusions (i.e., Are they substantially correlated? Do they form a reflexive or a formative construct?), their connection to related constructs (e.g., Are they distinguishable from intelligence or mathematical competence in a confirmatory factor analysis?), and the question of which of a person’s abilities can predict the correct solution of these brain teasers (by means of a regression analysis).

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Why Humans Fail in Solving the Monty Hall Dilemma: A Systematic Review

Cited by 11 publications

References 44 publications

Likelihood Neglect Bias and the Mental Simulations Approach: An Illustration using the Old and New Monty Hall Problems

Likelihood Neglect Bias and the Mental Simulations Approach: An Illustration using the Old and New Monty Hall Problems

Published benefits of ivermectin use in Itajaí, Brazil for COVID-19 infection, hospitalisation, and mortality are entirely explained by statistical artefacts

Tversky and Kahneman’s Cognitive Illusions: Who Can Solve Them, and Why?

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