The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to (...) infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue). (shrink)

The "two-envelopes" problem has stimulated much discussion on probabilistic reasoning, but relatively little experimentation. The problem specifies two identical envelopes, one of which contains twice as much money as the other. You are given one of the envelopes and the option of keeping it or trading for the other envelope. Variables of interest include the possible amounts of money involved, what is known about the process by which the amounts of money were assigned to the envelopes, and whether you are (...) allowed to know how much money is in the envelope in hand before deciding whether to keep or trade. In an earlier study, Butler and Nickerson found that when participants were allowed to know how much was in the envelope in hand, they generally elected to trade if that amount was small relative to the range of possibilities and to keep otherwise. The present experiments showed that this propensity was independent of the amount of money in the envelopes. Participants made decisions with a strong bias for avoiding the risk of losing by trading, particularly when the amount in hand was known and large relative to the range of possible amounts, regardless of the absolute value of the gamble. The results illustrate the dependence of thinking on the context in which it occurs, and demonstrate a tendency to treat quantities that are large or small relative to a particular context in which they are encountered as though they were large or small in a more general sense. (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)

The Two Envelopes Problem is a beautiful and quite confusing problem in decision theory which is ca. 35 years old and has provoked at least 150 papers directly addressing the problem and displaying a surprising variety of different responses. This paper finds decisive progress in an approach of Priest and Restall in 2003, contends that the recent papers having appeared since did not really go beyond that paper, argues further that Priest’s and Restall’s solution is still not complete, and proposes (...) a completion of their solution. If the analysis is correct, this work has the potential of laying the Two Envelopes Problem at rest. (shrink)

Previous claims to have resolved the two-envelope paradox have been premature. The paradoxical argument has been exposed as manifestly fallacious if there is an upper limit to the amount of money that may be put in an envelope; but the paradoxical cases which can be described if this limitation is removed do not involve mathematical error, nor can they be explained away in terms of the strangeness of infinity. Only by taking account of the partial sums of the infinite series (...) of expected gains can the paradox be resolved. (shrink)

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)