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.
Highlights
In the Monty Hall Problem (MHP), you know that the car you want is behind one of three closed doors and a goat behind the other two doors
Baumann (2005, 2008) produced a new argument based on a generalization of MHP: the Monty Hall Problem with two players (MHP2, see Table 1)
This paper describes the supposedly paradoxical solutions attributed to MHP2 from the perspective of a thorough Bayesian standpoint perspective
Summary
In the Monty Hall Problem (MHP), you know that the car you want is behind one of three closed doors and a goat behind the other two doors. Baumann (2005, 2008) produced a new argument based on a generalization of MHP: the Monty Hall Problem with two players (MHP2, see Table 1) In his view, the two players share the same initial state of knowledge, they eventually form two different probability distributions. This point of view is opposed by Levy (2007) and by Sprenger (2010) who rightly argue that the two players do not necessarily share the same state of knowledge throughout the game in particular when their original choices differ These authors do not explain the rationale of Baumann’s mistake and do not explicitly define the causal structure of MHP21. Explanations for the failure of researchers investigating MHP2 will be advanced and related to the “bias” that conducts psychologists to wrongly conclude that participants’ responses to MHP are of a non-Bayesian nature, that is, the neglect of the Bayesian standpoint (de Finetti, 1974)
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