, Volume 145, Issue 1, pp 89–109

Trying to Resolve the Two-Envelope Problem


    • Mathematics & Natural ScienceUniversity of Groningen
  • Barteld P. Kooi
    • Mathematics & Natural ScienceUniversity of Groningen
  • Willem Schaafsma
    • Mathematics & Natural ScienceUniversity of Groningen

DOI: 10.1007/s11229-004-7665-5

Cite this article as:
Albers, C.J., Kooi, B.P. & Schaafsma, W. Synthese (2005) 145: 89. doi:10.1007/s11229-004-7665-5


After explaining the well-known two-envelope ‘paradox’ by indicating the fallacy involved, we consider the two-envelope ‘problem’ of evaluating the ‘factual’ information provided to us in the form of the value contained by the envelope chosen first. We try to provide a synthesis of contributions from economy, psychology, logic, probability theory (in the form of Bayesian statistics), mathematical statistics (in the form of a decision-theoretic approach) and game theory. We conclude that the two-envelope problem does not allow a satisfactory solution. An interpretation is made for statistical science at large.

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© Springer 2005