The Two Envelope Paradox and Using Variables Within the Expectation Formula

Sorites (2008), vol. 20, p. 135-140.

Abstract

The present paper presents a diagnosis of what goes wrong in the reasoning in the “closed envelope” version of what is sometimes called “Two Envelope Paradox” or “Two Envelope Problem” or “Exchange Paradox”.  Plainly, some constraint on the use of variables within the expectation formula is necessary to escape the paradox.  We argue that previous proposed constraints are too restrictive: One can avoid the paradoxical reasoning as long as the conditional expectations of the relevant variables are the same in each event in the partition – provided that all the relevant equations are linear.

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