Trying to resolve the two-envelope problem

Albers, Casper J.; Kooi, Barteld P. and Schaafsma, Willem (2005). Trying to resolve the two-envelope problem. Synthese, 145(1) pp. 89–109.

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

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.