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  1. Casper J. Albers, Barteld P. Kooi & Willem Schaafsma (2005). Trying to Resolve the Two-Envelope Problem. Synthese 145 (1):89 - 109.
    After explaining the well-known two-envelope paradox by indicating the fallacy involved, we consider the two-envelope problem of evaluating the factual information provided to us in the form of the value contained by the envelope chosen first. We try to provide a synthesis of contributions from economy, psychology, logic, probability theory (in the form of Bayesian statistics), mathematical statistics (in the form of a decision-theoretic approach) and game theory. We conclude that the two-envelope problem does not allow a satisfactory solution. An (...)
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  2. Frank Arntzenius, Adam Elga & and John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251-283.
    We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as ‘Trumped’ (Arntzenius and McCarthy 1997), ‘Rouble trouble’ (Arntzenius and Barrett 1999), ‘The airtight Dutch book’ (McGee 1999), and ‘The two envelopes puzzle’ (Broome 1999). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...)
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  3. Frank Arntzenius, Adam Elga & John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251 - 283.
    We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as 'Trumped' (Arntzenius and McCarthy 1997), 'Rouble trouble' (Arntzenius and Barrett 1999), 'The airtight Dutch book' (McGee 1999), and 'The two envelopes puzzle' (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...)
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  4. Frank Arntzenius & David McCarthy (1997). The Two Envelope Paradox and Infinite Expectations. Analysis 57 (1):42–50.
    The two envelope paradox can be dissolved by looking closely at the connection between conditional and unconditional expectation and by being careful when summing an infinite series of positive and negative terms. The two envelope paradox is not another St. Petersburg paradox and that one does not need to ban talk of infinite expectation values in order to dissolve it. The article ends by posing a new puzzle to do with infinite expectations.
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  5. Fc Boogerd, Fj Bruggeman & Rc Richardson (2005). Casper J. Albers, Barteld P. Kooi and Willem Schaafsma/Trying to Resolve the Two-Envelope Problem Edwin H.-C. Hung/Projective Explanation: How Theories Explain Empirical Data in Spite of Theory. [REVIEW] Synthese 145 (1):499-500.
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  6. John Broome (1995). The Two-Envelope Paradox. Analysis 55 (1):6 - 11.
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  7. Bruce D. Burns (forthcoming). Probabilistic Reasoning in the Two-Envelope Problem. Thinking and Reasoning:1-22.
    In the two-envelope problem, a reasoner is offered two envelopes, one containing exactly twice the money in the other. After observing the amount in one envelope, it can be traded for the unseen contents of the other. It appears that it should not matter whether the envelope is traded, but recent mathematical analyses have shown that gains could be made if trading was a probabilistic function of amount observed. As a problem with a purely probabilistic solution, it provides a potentially (...)
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  8. James Cargile (1992). On a Problem About Probability and Decision. Analysis 52 (4):211 - 216.
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  9. Paul Castell & Diderik Batens (1994). The Two Envelope Paradox: The Infinite Case. Analysis 54 (1):46 - 49.
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  10. David J. Chalmers, The Two-Envelope Paradox: A Complete Analysis?
    A wealthy eccentric places two envelopes in front of you. She tells you that both envelopes contain money, and that one contains twice as much as the other, but she does not tell you which is which. You are allowed to choose one envelope, and to keep all the money you find inside.
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  11. David J. Chalmers (2002). The St. Petersburg Two-Envelope Paradox. Analysis 62 (274):155–157.
    I reason: (1) For any x, if I knew that A contained x, then the odds are even that B contains either 2x or x/2, so the expected amount in B would be 5x/4. So (2) for all x, if I knew that A contained x, I would have an expected gain in switching to B. So (3) I should switch to B. But this seems clearly wrong, as my information about A and B is symmetrical.
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  12. James Chase (2002). The Non-Probabilistic Two Envelope Paradox. Analysis 62 (2):157–160.
    Given a choice between two sealed envelopes, one of which contains twice as much money as the other (and in any case some), you don't know which contains the larger sum and so choose one at random. You are then given the option of taking the other envelope instead. Is it rational to do so? Surely not. but a specious line of reasoning suggests otherwise.
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  13. Charles S. Chihara (1995). The Mystery of Julius: A Paradox in Decision Theory. Philosophical Studies 80 (1):1 - 16.
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  14. Michael Clark & Nicholas Shackel (2003). Decision Theory, Symmetry and Causal Structure: Reply to Meacham and Weisberg. Mind 112 (448):691-701.
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  15. Michael Clark & Nicholas Shackel (2000). The Two-Envelope Paradox. Mind 109 (435):415--442.
    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 (...)
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  16. Monte Cook (2002). Getting Clear on the Two-Envelope Paradox. Southwest Philosophy Review 18 (1):45-51.
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  17. Franz Dietrich & Christian List (2005). The Two-Envelope Paradox: An Axiomatic Approach. Mind 114 (454):239-248.
    There has been much discussion on the two-envelope paradox. Clark and Shackel (2000) have proposed a solution to the paradox, which has been refuted by Meacham and Weisberg (2003). Surprisingly, however, the literature still contains no axiomatic justification for the claim that one should be indifferent between the two envelopes before opening one of them. According to Meacham and Weisberg, "decision theory does not rank swapping against sticking [before opening any envelope]" (p. 686). To fill this gap in the literature, (...)
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  18. Igor Douven (2007). A Three-Step Solution to the Two-Envelope Paradox. Logique Et Analyse 50 (200):359.
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  19. James Dreier (forthcoming). Boundless Good. Ms.
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  20. Don Fallis (2009). Taking the Two Envelope Paradox to the Limit. Southwest Philosophy Review 25 (2):95-111.
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  21. Paul Franceschi, Le Paradoxe Des Deux Enveloppes Et le Choix de L'Indifférence.
    I present in this paper a solution to the Two-Envelope Paradox. I begin with stating the paradox and describing some related experiments. I justify then the fact that choosing either envelope is indifferent. I also point out the flaw in the reasoning inherent to the two-envelope paradox.
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  22. R. B. Gardner (2000). The Exchange Paradox, Finite Additivity, and the Principle of Dominance Commentary. Poznan Studies in the Philosophy of the Sciences and the Humanities 71:49-76.
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  23. Olav Gjelsvik (2002). Paradox Lost, but in Which Envelope? Croatian Journal of Philosophy 2 (3):353-362.
    The aim of this paper is to diagnose the so-called two envelopes paradox. Many writers have claimed that there is something genuinely paradoxical in the situation with the two envelopes, and some writers are now developing non-standards theories of expected utility. I claim that there is no paradox for expected utility theory as I understand that theory, and that contrary claims are confused. Expected utility theory is completely unaffected by the two-envelope paradox.
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  24. Jeremy Gwiazda (2012). Repeated St Petersburg Two-Envelope Trials and Expected Value. The Reasoner 6 (3).
    It is commonly believed that when a finite value is received in a game that has an infinite expected value, it is in one’s interest to redo the game. We have argued against this belief, at least in the repeated St Petersburg two-envelope case. We also show a case where repeatedly opting for a higher expected value leads to a worse outcome.
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  25. Terry Horgan, The Two Envelope Paradox and the Foundations of Rational Decision Theory.
    You are given a choice between two envelopes. You are told, reliably, that each envelope has some money in it—some whole number of dollars, say—and that one envelope contains twice as much money as the other. You don’t know which has the higher amount and which has the lower. You choose one, but are given the opportunity to switch to the other. Here is an argument that it is rationally preferable to switch: Let x be the quantity of money in (...)
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  26. Terry Horgan (2000). The Two-Envelope Paradox, Nonstandard Expected Utility, and the Intensionality of Probability. Noûs 34 (4):578–603.
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  27. Frank Jackson, Peter Menzies & Graham Oppy (1994). The Two Envelope 'Paradox'. Analysis 54 (1):43 - 45.
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  28. B. D. Katz & D. Olin (2010). Conditionals, Probabilities, and Utilities: More on Two Envelopes. Mind 119 (473):171-183.
    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, (...)
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  29. Bernard D. Katz & Doris Olin (2007). A Tale of Two Envelopes. Mind 116 (464):903-926.
    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. (...)
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  30. C. Lee (2013). The Two-Envelope Paradox: Asymmetrical Cases. Mind 122 (485):1-26.
    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 (...)
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  31. Gary Malinas (2006). Two Envelope Problems. The Proceedings of the Twenty-First World Congress of Philosophy 9:153-158.
    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 (...)
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  32. Gary Malinas (2003). Two Envelope Problems and the Roles of Ignorance. Acta Analytica 18 (1-2):217-225.
    Four variations on Two Envelope Paradox are stated and compared. The variations are employed to provide a diagnosis and an explanation of what has gone awry in the paradoxical modeling of the decision problem that the paradox poses. The canonical formulation of the paradox underdescribes the ways in which one envelope can have twice the amount that is in the other. Some ways one envelope can have twice the amount that is in the other make it rational to prefer the (...)
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  33. Timothy J. McGrew, David Shier & Harry S. Silverstein (1997). The Two-Envelope Paradox Resolved. Analysis 57 (1):28–33.
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  34. Christopher J. G. Meacham & Jonathan Weisberg (2003). Clark and Shackel on the Two-Envelope Paradox. Mind 112 (448):685-689.
    Clark and Shackel have recently argued that previous attempts to resolve the two-envelope paradox fail, and that we must look to symmetries of the relevant expected-value calculations for a solution. Clark and Shackel also argue for a novel solution to the peeking case, a variant of the two-envelope scenario in which you are allowed to look in your envelope before deciding whether or not to swap. Whatever the merits of these solutions, they go beyond accepted decision theory, even contradicting it (...)
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  35. Raymond S. Nickerson & Susan F. Butler (2011). Keep or Trade? An Experimental Study of the Exchange Paradox. Thinking and Reasoning 14 (4):365-394.
    The “exchange paradox”—also referred to in the literature by a variety of other names, notably the “two-envelopes problem”—is notoriously difficult, and experts are not all agreed as to its resolution. Some of the various expressions of the problem are open to more than one interpretation; some are stated in such a way that assumptions are required in order to fill in missing information that is essential to any resolution. In three experiments several versions of the problem were used, in each (...)
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  36. Raymond S. Nickerson, Susan F. Butler, Nathaniel Delaney-Busch & Michael Carlin (2014). Keep or Trade? Effects of Pay-Off Range on Decisions with the Two-Envelops Problem. Thinking and Reasoning 20 (4):472-499.
    The ?two-envelops? 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 (...)
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  37. Raymond S. Nickerson & Ruma Falk (2006). The Exchange Paradox: Probabilistic and Cognitive Analysis of a Psychological Conundrum. Thinking and Reasoning 12 (2):181 – 213.
    The term “exchange paradox” refers to a situation in which it appears to be advantageous for each of two holders of an envelope containing some amount of money to always exchange his or her envelope for that of the other individual, which they know contains either half or twice their own amount. We review several versions of the problem and show that resolving the paradox depends on the specifics of the situation, which must be disambiguated, and on the player's beliefs. (...)
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  38. John Norton (1998). Where the Sum of Our Expectation Fails Us: The Exchange Paradox. Pacific Philosophical Quarterly 79 (1):34–58.
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  39. Graham Priest & Greg Restall, Envelopes and Indifference.
    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. (...)
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  40. P. Rawling (1994). A Note on the Two Envelopes Problem. Theory and Decision 36 (1):97-102.
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  41. Piers Rawling (2000). The Exchange Paradox, Finite Additivity, and the Principle of Dominance. Poznan Studies in the Philosophy of the Sciences and the Humanities 71:49-76.
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  42. Piers Rawling (1997). Perspectives on a Pair of Envelopes. Theory and Decision 43 (3):253-277.
    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 (...)
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  43. Melinda A. Roberts (2009). The Nonidentity Problem and the Two Envelope Problem: When is One Act Better for a Person Than Another? In David Wasserman & Melinda Roberts (eds.), Harming Future Persons. Springer. 201--228.
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  44. W. Schaafsma, B. P. Kooi & C. Albers (2005). Trying to Resolve the Two-Envelope Problem. Synthese 145 (1):89-109.
    After explaining the well-known two-envelope 'paradox' by indicating the fallacy involved, we consider the two-envelope 'problem' of evaluating the 'factual' information provided to us in the form of the value contained by the envelope chosen first. We try to provide a synthesis of contributions from economy, psychology, logic, probability theory (in the form of Bayesian statistics), mathematical statistics (in the form of a decision-theoretic approach) and game theory. We conclude that the two-envelope problem does not allow a satisfactory solution. An (...)
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  45. Eric Schwitzgebel & Josh Dever (2008). The Two Envelope Paradox and Using Variables Within the Expectation Formula. Sorites:135-140.
    You are presented with a choice between two envelopes. You know one envelope contains twice as much money as the other, but you don't know which contains more. You arbitrarily choose one envelope -- call it Envelope A -- but don't open it. Call the amount of money in that envelope X. Since your choice was arbitrary, the other envelope (Envelope B) is 50% likely to be the envelope with more and 50% likely to be the envelope with less. But, (...)
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  46. Alexander D. Scott & Michael Scott (1997). What’s in the Two Envelope Paradox? Analysis 57 (1):34–41.
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  47. Jordan Howard Sobel (1994). Two Envelopes. Theory and Decision 36 (1):69-96.
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  48. P. A. Sutton (2010). The Epoch of Incredulity: A Response to Katz and Olin's 'A Tale of Two Envelopes'. Mind 119 (473):159-169.
    When David Lewis ( 1986 ) told us that possible worlds were a ‘paradise for philosophers’, he neglected to add that they are a minefield for decision theorists. Possibilities — be they nomological, metaphysical, or epistemic possibilities — have little to do with subjective probabilities, and it is these latter that matter most to decision theory. Bernard Katz and Doris Olin ( 2007 ) have tried to solve the two-envelope problem by appealing to possible worlds and counterfactual conditionals. In this (...)
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  49. P. A. Sutton (2010). The Epoch of Incredulity. Mind 119 (473):159-169.
    When David Lewis (1986) told us that possible worlds were a ‘paradise for philosophers,’ he neglected to add that they are a minefield for decision theorists. Possibilities—be they nomological, metaphysical, or epistemic possibilities—have little to do with subjective probabilities, and it is these latter that matter most to decision theory. Bernard Katz and Doris Olin (2007) have tried to solve the two-envelope problem by appealing to possible worlds and counterfactual conditionals. In this paper I explain why any such attempt is (...)
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  50. Paul Syverson (2010). Opening Two Envelopes. Acta Analytica 25 (4):479-498.
    In the two-envelope problem, one is offered a choice between two envelopes, one containing twice as much money as the other. After seeing the contents of the chosen envelope, the chooser is offered the opportunity to make an exchange for the other envelope. However, it appears to be advantageous to switch, regardless of what is observed in the chosen envelope. This problem has an extensive literature with connections to probability and decision theory. The literature is roughly divided between those that (...)
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