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Landau’s switching problem: An elementary decision theoretic resolution of the two-envelope paradox

Research output: Working paperDiscussion paper

Original languageEnglish
Unpublished28 Sep 2019


  • Two-envelope problem

    Two_envelope_problem.pdf, 202 KB, application/pdf

    Uploaded date:28 Sep 2019

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King's Authors


In this short note, I provide an elementary decision theoretic resolution of Landau's switching problem, which is also known as the two-envelope paradox. I show that there are no general arguments for or against switching, which confirms the common intuition. This result does not depend on whether we assume the existence of probabilities or not. Nor does it depend on the variations of the problem in which the decision maker opens the first envelope or not. I also give an explanation for why (i) the popular argument for switching is actually right, though it is only part of a larger decision problem, and (ii) the fragmented literature on this problem does not necessarily mean that some opposing approaches to the problem are wrong.

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