Two Envelope Problems

When decision makers have more to gain than to lose by changing their minds, and that is the only relevant fact, they thereby have a reason to change their minds. While this is sage advice, it is silent on when one stands more to gain than to lose. The two envelope paradox provides a case where the appearance of advantage in changing your mind is resilient despite being a chimera. Setups that are unproblematically modeled by decision tables that are used in the formulation of the two envelope paradox are described, and variations on them are stipulated. The problems posed by the paradoxical modeling are then contrasted with the variations. The paper concludes with a brief explanation of why the paradoxical modeling does not gain support from the fact that one envelope has twice the amount that is in the other
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