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Trying to Resolve the Two-Envelope Problem

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Abstract

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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Authors and Affiliations

  1. Mathematics & Natural Science, University of Groningen, P.O. Box 800, 9700, AV, Groningen, The Netherlands

    Casper J. Albers, Barteld P. Kooi & Willem Schaafsma

Authors
  1. Casper J. Albers
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  2. Barteld P. Kooi
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  3. Willem Schaafsma
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Correspondence to Casper J. Albers.

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Albers, C.J., Kooi, B.P. & Schaafsma, W. Trying to Resolve the Two-Envelope Problem. Synthese 145, 89–109 (2005). https://doi.org/10.1007/s11229-004-7665-5

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