Rationality, the Bayesian standpoint, and the Monty-Hall problem

Abstract

The Monty-Hall Problem (MHP) has been used to argue against a subjectivist view of Bayesianism in two ways. First, psychologists have used it to illustrate that people do not revise their degrees of belief in line with experimenters' application of Bayes' rule. Second, philosophers view MHP and its two-player extension (MHP2) as evidence that probabilities cannot be applied to single cases. Both arguments neglect the Bayesian standpoint, which requires that MHP2 (studied here) be described in different terms than usually applied and that the initial set of possibilities be stable (i.e., a focusing situation). This article corrects these errors and reasserts the Bayesian standpoint; namely, that the subjective probability of an event is always conditional on a belief reviser's specific current state of knowledge.

The Psychology of Uncertainty and Three-Valued Truth Tables

“…Is there a normative framework for unifying all these experimental results? We have argued (Baratgin, 2015 ; Baratgin and Politzer, 2016 ; Over and Baratgin, 2017 ; Over and Cruz, 2018 ) that de Finetti's Bayesian subjective theory offers just such a framework. De Finetti is one of the founding fathers of modern probability theory, and the most prominent representative of subjective Bayesianism.…”

“…De Finetti is one of the founding fathers of modern probability theory, and the most prominent representative of subjective Bayesianism. His overall approach to probability (de Finetti, 1974 ) has deep psychological relevance (see Baratgin and Politzer, 2006 , 2007 ; Baratgin, 2015 , for a discussion in the field of the psychology of probability judgment). His conception of probability as subjective degree of belief, and of the assessment of probability through the well-known betting procedure, are rooted in psychological reflection.…”

“…This level corresponds to the full range of subjective degrees of belief about events where the initial ignorance and the ensuing uncertainty give way to the expression of additive probabilities. Fine distinctions are thus possible at Level 2, which is of psychological importance, since both ordinary people and scientists do often distinguish between events that are uncertain, judging some as more probable than others conditionally on their personal state of knowledge (Baratgin, 2015 ).…”

Editorial: Improving Bayesian Reasoning: What Works and Why?

“…Others point to a lack of due attention to individual differences in reasoning and to the cognitive processes that lead to final estimates (Johnson and Tubau, 2015 ; McNair, 2015 ; Vallée-Tourangeau et al, 2015 ). Baratgin ( 2015 ) and Mandel ( 2014a ) both take Bayesian researchers to task over their disregard of the subjectivist (and coherence-centered) foundations of Bayesianism.…”

“…However, attention to problems that have a temporal component is not lacking in this collection: Tubau et al ( 2015 ) provide an insightful and comprehensive review of the Monty Hall Problem and Baratgin ( 2015 ) uses the two-player version of that problem to expose logical and terminological breakdowns in earlier theoretical analyses. Mandel ( 2014b ) explores the perhaps even more complex Sleeping Beauty problem, which involves belief revision under conditions of asynchrony, to highlight how visual representations using quasi-logic trees can help clarify points of philosophical disagreement in the literature.…”