The Two Envelope Paradox: The Infinite Case
Jackson, Menzies and Oppy conclude their paper (above) with the following comment: 'Our diagnosis of where the reasoning in the original case goes astray depended on the fact that the subject knows that the amount of money is bounded top and bottom. This assumption could be dispensed with in fantastical cases... It would still be wrong to prefer one envelope over the other. However, we cannot offer the same diagnosis of the error in the expected value calculation to the opposite conclusion... we can reasonably insist that "the standard method" for probabilistic and expected value reasoning ought not to be applied in such cases.' It seems to us that it is precisely in these 'fantastical' cases that the Two Envelope Paradox is a serious conceptual challenge.1 We show that the paradox can indeed be tackled in the infinite case using 'standard methods'.