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The Monty-Hall Problem (MHP) challenges Bayesianism, but this study reasserts the Bayesian standpoint. Subjective probabilities are always conditional on an individual's current knowledge state, even in complex scenarios like MHP 2.

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Area of Science:

  • Decision-making and Probability Theory
  • Cognitive Psychology
  • Philosophy of Science

Background:

  • The Monty-Hall Problem (MHP) is frequently used to critique subjectivist Bayesianism.
  • Psychologists cite MHP to show belief revision discrepancies with Bayes' rule.
  • Philosophers use MHP and its extension (MHP 2) to question single-case probability application.

Purpose of the Study:

  • To reassert the Bayesian standpoint concerning the Monty-Hall Problem and its two-player extension (MHP 2).
  • To correct common misinterpretations of MHP within psychological and philosophical arguments.
  • To clarify the conditional nature of subjective probability in belief revision.

Main Methods:

  • Re-evaluation of the standard description of MHP 2.
  • Application of Bayesian principles under conditions of stable initial possibilities (focusing situations).
  • Analysis of subjective probability as conditional on the specific state of knowledge.

Main Results:

  • Common arguments against subjectivist Bayesianism using MHP are based on flawed interpretations.
  • MHP 2 requires a specific description and stable initial possibilities for valid Bayesian analysis.
  • Subjective probability is fundamentally dependent on the current knowledge state of the belief reviser.

Conclusions:

  • The Bayesian standpoint remains robust when MHP and MHP 2 are correctly framed.
  • Psychological and philosophical critiques of Bayesianism based on MHP are often misguided.
  • Subjective probability is inherently dynamic and context-dependent, aligning with the Bayesian conditional approach.