Trying to Resolve the Two-Envelope Problem

Authors: Albers, Casper¹; Kooi, Barteld²; Schaafsma, Willem²

Source: Synthese, Volume 145, Number 1, May 2005 , pp. 89-109(21)

Publisher: Springer

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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.

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11229-004-7665-5

Affiliations: 1: Mathematics & Natural Science, University of Groningen, P.O. Box 800, 9700, AV, Groningen, The Netherlands, Email: casper@math.rug.nl 2: Mathematics & Natural Science, University of Groningen, P.O. Box 800, 9700, AV, Groningen, The Netherlands,

Publication date: 2005-05-01