In the asymmetrical variant of the two-envelope paradox, the amount in envelope A is determined first, and then the amount in envelope B is determined to be either twice or half the amount in A by flipping a fair coin. Contra the common belief that B is preferable to A in this case, I show that the proposed arguments for this common belief all fail, and argue that B is not preferable to A if the expected values of the amounts (...) in the envelopes are infinite. Using the examples I deploy in my arguments against the common belief, I also refute certain proposed solutions to the two-envelope paradox and draw some general lessons. (shrink)

Sutton ( 2010 ) claims that on our analysis (2007), the problem in the two-envelope paradox is an error in counterfactual reasoning. In fact, we distinguish two formulations of the paradox, only one of which, on our account, involves an error in conditional reasoning. According to Sutton, it is conditional probabilities rather than subjunctive conditionals that are essential to the problem. We argue, however, that his strategy for assigning utilities on the basis of conditional probabilities leads to absurdity. In addition, (...) we show that a crucial presupposition of Sutton’s argument — namely, that one can know that envelope A contains n simply on the basis of a stipulation — is mistaken. (shrink)

This paper deals with the two-envelope paradox. Two main formulations of the paradoxical reasoning are distinguished, which differ according to the partition of possibilities employed. We argue that in the first formulation the conditionals required for the utility assignment are problematic; the error is identified as a fallacy of conditional reasoning. We go on to consider the second formulation, where the epistemic status of certain singular propositions becomes relevant; our diagnosis is that the states considered do not exhaust the possibilities. (...) Thus, on our approach to the paradox, the fallacy, in each formulation, is found in the reasoning underlying the relevant utility matrix; in both cases, the paradoxical argument goes astray before one gets to questions of probability or calculations of expected utility. (shrink)

This paper discusses the finite version of the two envelope paradox. (That is, we treat the paradox against the background assumption that there is only a finite amount of money in the world.).

This volume consists of the invited papers presented at the 23rd International Wittgenstein Conference held in Kirchberg, Austria in August 2000. Among the topics treated are: truth, psychologism, science, the nature of rational discourse, practical reason, contextualism, vagueness, types of rationality, the rationality of religious belief, and Wittgenstein. Questions addressed include: Is rationality tied to special sorts of contexts? ls rationality tied to language? Is scientific rationality the only kind of rationality? Is there something like a Western rationality? and: Could (...) we genetically engineer human beings to be less wicked? (shrink)

Consider this situation: Here are two envelopes. You have one of them. Each envelope contains some quantity of money, which can be of any positive real magnitude. One contains twice the amount of money that the other contains, but you do not know which one. You can keep the money in your envelope, whose numerical value you do not know at this stage, or you can exchange envelopes and have the money in the other. You wish to maximise your money. (...) What should you do?1 Here are three forms of reasoning about this situation, which we shall call.. (shrink)