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  1. Exceeding Expectations: Stochastic Dominance as a General Decision Theory.Christian Tarsney - manuscript
    The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty (...)
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  2. Can an evidentialist be risk-averse?Hayden Wilkinson - manuscript
    Two key questions of normative decision theory are: 1) whether the probabilities relevant to decision theory are evidential or causal; and 2) whether agents should be risk-neutral, and so maximise the expected value of the outcome, or instead risk-averse (or otherwise sensitive to risk). These questions are typically thought to be independent---that our answer to one bears little on our answer to the other. But there is a surprising argument that they are not. In this paper, I show that evidential (...)
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  3. Chaos, ad infinitum.Hayden Wilkinson - manuscript
    Our universe is both chaotic and (most likely) infinite in space and time. But it is within this setting that we must make moral decisions. This presents problems. The first: due to our universe's chaotic nature, our actions often have long-lasting, unpredictable effects; and this means we typically cannot say which of two actions will turn out best in the long run. The second problem: due to the universe's infinite dimensions, and infinite population therein, we cannot compare outcomes by simply (...)
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  4. Boundless Good.James Dreier - forthcoming - Ms.
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  5. Pascalian Expectations and Explorations.Alan Hajek & Elizabeth Jackson - forthcoming - In Roger Ariew & Yuval Avnur (eds.), The Blackwell Companion to Pascal. Wiley-Blackwell.
    Pascal’s Wager involves expected utilities. In this chapter, we examine the Wager in light of two main features of expected utility theory: utilities and probabilities. We discuss infinite and finite utilities, and zero, infinitesimal, extremely low, imprecise, and undefined probabilities. These have all come up in recent literature regarding Pascal’s Wager. We consider the problems each creates and suggest prospects for the Wager in light of these problems.
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  6. An Epistemic Version of Pascal's Wager.Elizabeth Jackson - forthcoming - Journal of the American Philosophical Association:1-17.
    Epistemic consequentialism is the view that epistemic goodness is more fundamental than epistemic rightness. This paper examines the relationship between epistemic consequentialism and theistic belief. I argue that, in an epistemic consequentialist framework, there is an epistemic reason to believe in God. Imagine having an unlimited amount of time to ask an omniscient being anything you wanted. The potential epistemic benefits would be enormous. Considerations like these point to an epistemic version of Pascal’s wager. I compare and contrast the epistemic (...)
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  7. A Puzzle about Sums.Andrew Y. Lee - forthcoming - Oxford Studies in Metaphysics.
    A famous mathematical theorem says that the sum of an infinite series of numbers can depend on the order in which those numbers occur. Suppose we interpret the numbers in such a series as representing instances of some physical quantity, such as the weights of a collection of items. The mathematics seems to lead to the result that the weight of a collection of items can depend on the order in which those items are weighed. But that is very hard (...)
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  8. Egyptology and Fanaticism.Hayden Wilkinson - forthcoming - Philosophical Studies.
    Various decision theories share a troubling implication. They imply that, for any finite amount of value, it would be better to wager it all for a vanishingly small probability of some greater value. Counterintuitive as it might be, this fanaticism has seemingly compelling independent arguments in its favour. In this paper, I consider perhaps the most prima facie compelling such argument: an Egyptology argument (an analogue of the Egyptology argument from population ethics). I show that, despite recent objections from Russell (...)
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  9. Unbounded Utility.Zachary Goodsell - 2023 - Dissertation, University of Southern California
  10. Infinite Aggregation and Risk.Hayden Wilkinson - 2023 - Australasian Journal of Philosophy 101 (2):340-359.
    For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...)
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  11. Money-Pump Arguments.Johan E. Gustafsson - 2022 - Cambridge: Cambridge University Press.
    Suppose that you prefer A to B, B to C, and C to A. Your preferences violate Expected Utility Theory by being cyclic. Money-pump arguments offer a way to show that such violations are irrational. Suppose that you start with A. Then you should be willing to trade A for C and then C for B. But then, once you have B, you are offered a trade back to A for a small cost. Since you prefer A to B, you (...)
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  12. In Defense of Fanaticism.Hayden Wilkinson - 2022 - Ethics 132 (2):445-477.
    Which is better: a guarantee of a modest amount of moral value, or a tiny probability of arbitrarily large value? To prefer the latter seems fanatical. But, as I argue, avoiding such fanaticism brings severe problems. To do so, we must decline intuitively attractive trade-offs; rank structurally identical pairs of lotteries inconsistently, or else admit absurd sensitivity to tiny probability differences; have rankings depend on remote, unaffected events ; and often neglect to rank lotteries as we already know we would (...)
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  13. How to co-exist with nonexistent expectations.Randall G. McCutcheon - 2021 - Synthese 198 (3):2783-2799.
    Dozens of articles have addressed the challenge that gambles having undefined expectation pose for decision theory. This paper makes two contributions. The first is incremental: we evolve Colyvan's ``Relative Expected Utility Theory'' into a more viable ``conservative extension of expected utility theory" by formulating and defending emendations to a version of this theory proposed by Colyvan and H\'ajek. The second is comparatively more surprising. We show that, so long as one assigns positive probability to the theory that there is a (...)
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  14. Infinite Prospects.Jeffrey Sanford Russell & Yoaav Isaacs - 2021 - Philosophy and Phenomenological Research 103 (1):178-198.
    People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...)
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  15. Too much of a good thing: decision-making in cases with infinitely many utility contributions.Christopher J. G. Meacham - 2020 - Synthese 198 (8):7309-7349.
    Theories that use expected utility maximization to evaluate acts have difficulty handling cases with infinitely many utility contributions. In this paper I present and motivate a way of modifying such theories to deal with these cases, employing what I call “Direct Difference Taking”. This proposal has a number of desirable features: it’s natural and well-motivated, it satisfies natural dominance intuitions, and it yields plausible prescriptions in a wide range of cases. I then compare my account to the most plausible alternative, (...)
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  16. Non-Archimedean Preferences Over Countable Lotteries.Jeffrey Sanford Russell - 2020 - Journal of Mathematical Economics 88 (May 2020):180-186.
    We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.
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  17. Salvaging Pascal’s Wager.Elizabeth Jackson & Andrew Rogers - 2019 - Philosophia Christi 21 (1):59-84.
    Many think that Pascal’s Wager is a hopeless failure. A primary reason for this is because a number of challenging objections have been raised to the wager, including the “many gods” objection and the “mixed strategy” objection. We argue that both objections are formal, but not substantive, problems for the wager, and that they both fail for the same reason. We then respond to additional objections to the wager. We show how a version of Pascalian reasoning succeeds, giving us a (...)
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  18. Aggregation for potentially infinite populations without continuity or completeness.David McCarthy, Kalle M. Mikkola & J. Teruji Thomas - 2019 - arXiv:1911.00872 [Econ.TH].
    We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to (...)
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  19. Difference Minimizing Theory.Christopher J. G. Meacham - 2019 - Ergo: An Open Access Journal of Philosophy 6.
    Standard decision theory has trouble handling cases involving acts without finite expected values. This paper has two aims. First, building on earlier work by Colyvan (2008), Easwaran (2014), and Lauwers and Vallentyne (2016), it develops a proposal for dealing with such cases, Difference Minimizing Theory. Difference Minimizing Theory provides satisfactory verdicts in a broader range of cases than its predecessors. And it vindicates two highly plausible principles of standard decision theory, Stochastic Equivalence and Stochastic Dominance. The second aim is to (...)
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  20. Infinity in ethics (2nd edition).Peter Vallentyne & Daniel Rubio - 2019 - Routledge Encyclopedia of Philosophy.
    Puzzles can arise in value theory and deontic (permissibility) theory when infinity is involved. These puzzles can arise for ethics, for prudence, or for any normative perspective. For the sake of simplicity, we focus on the ethical versions of these problems. We start by addressing problems that can arise in determining what is permissible, either in a given choice situation when there are an infinite number of options or in infinite sequence of choice situations, each with only finitely many options. (...)
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  21. Pascal’s Wager.Paul F. A. Bartha & Lawrence Pasternack (eds.) - 2018 - New York: Cambridge University Press.
    In his famous Wager, Blaise Pascal offers the reader an argument that it is rational to strive to believe in God. Philosophical debates about this classic argument have continued until our own times. This volume provides a comprehensive examination of Pascal's Wager, including its theological framework, its place in the history of philosophy, and its importance to contemporary decision theory. The volume starts with a valuable primer on infinity and decision theory for students and non-specialists. A sequence of chapters then (...)
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  22. Infinite Value and the Best of All Possible Worlds.Nevin Climenhaga - 2018 - Philosophy and Phenomenological Research 97 (2):367-392.
    A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already created. (...)
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  23. God meets Satan’s Apple: the paradox of creation.Rubio Daniel - 2018 - Philosophical Studies 175 (12):2987-3004.
    It is now the majority view amongst philosophers and theologians that any world could have been better. This places the choice of which world to create into an especially challenging class of decision problems: those that are discontinuous in the limit. I argue that combining some weak, plausible norms governing this type of problem with a creator who has the attributes of the god of classical theism results in a paradox: no world is possible. After exploring some ways out of (...)
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  24. Expected Comparative Utility Theory: A New Theory of Rational Choice.David Robert - 2018 - Philosophical Forum 49 (1):19-37.
    In this paper, I argue for a new normative theory of rational choice under risk, namely expected comparative utility (ECU) theory. I first show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility (CU) of a in G—that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this (...)
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  25. The Relatively Infinite Value of the Environment.Paul Bartha & C. Tyler DesRoches - 2017 - Australasian Journal of Philosophy 95 (2):328-353.
    Some environmental ethicists and economists argue that attributing infinite value to the environment is a good way to represent an absolute obligation to protect it. Others argue against modelling the value of the environment in this way: the assignment of infinite value leads to immense technical and philosophical difficulties that undermine the environmentalist project. First, there is a problem of discrimination: saving a large region of habitat is better than saving a small region; yet if both outcomes have infinite value, (...)
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  26. A Thoroughly Modern Wager.Michael J. Shaffer - 2017 - Logos and Episteme 8 (2):207-231.
    This paper presents a corrected version of Pascal's wager that makes it consonant with modern decision theory. The corrected wager shows that not committing to God's existence is the rational choice.
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  27. Making Do Without Expectations.Paul F. A. Bartha - 2016 - Mind 125 (499):799-827.
    The Pasadena game invented by Nover and Hájek raises a number of challenges for decision theory. The basic problem is how the game should be evaluated: it has no expectation and hence no well-defined value. Easwaran has shown that the Pasadena game does have a weak expectation, raising the possibility that we can eliminate the value gap by requiring agents to value gambles at their weak expectations. In this paper, I first prove a negative result: there are gambles like the (...)
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  28. Probabilities Cannot Be Rationally Neglected.Yoaav Isaacs - 2016 - Mind 125 (499):759-762.
    In response to Smith, I argue that probabilities cannot be rationally neglected. I show that Smith’s proposal for ignoring low-probability outcomes must, on pain of violating dominance reasoning, license taking arbitrarily high risk for arbitrarily little reward.
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  29. Wagering Against Divine Hiddenness.Elizabeth Jackson - 2016 - European Journal for Philosophy of Religion 8 (4):85-108.
    J.L. Schellenberg argues that divine hiddenness provides an argument for the conclusion that God does not exist, for if God existed he would not allow non-resistant non-belief to occur, but non-resistant non-belief does occur, so God does not exist. In this paper, I argue that the stakes involved in theistic considerations put pressure on Schellenberg’s premise that non-resistant non-belief occurs. First, I specify conditions for someone’s being a resistant non-believer. Then, I argue that many people fulfill these conditions because, given (...)
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  30. Infinite Decisions and Rationally Negligible Probabilities.Nicholas J. J. Smith - 2016 - Mind (500):1-14.
    I have argued for a picture of decision theory centred on the principle of Rationally Negligible Probabilities. Isaacs argues against this picture on the grounds that it has an untenable implication. I first examine whether my view really has this implication; this involves a discussion of the legitimacy or otherwise of infinite decisions. I then examine whether the implication is really undesirable and conclude that it is not.
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  31. Unexpected Expectations.Alan Hájek - 2014 - Mind 123 (490):533-567.
    A decade ago, Harris Nover and I introduced the Pasadena game, which we argued gives rise to a new paradox in decision theory even more troubling than the St Petersburg paradox. Gwiazda's and Smith's articles in this volume both offer revisionist solutions. I critically engage with both articles. They invite reflections on a number of deep issues in the foundations of decision theory, which I hope to bring out. These issues include: some ways in which orthodox decision theory might be (...)
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  32. Is Evaluative Compositionality a Requirement of Rationality?Nicholas J. J. Smith - 2014 - Mind 123 (490):457-502.
    This paper presents a new solution to the problems for orthodox decision theory posed by the Pasadena game and its relatives. I argue that a key question raised by consideration of these gambles is whether evaluative compositionality (as I term it) is a requirement of rationality: is the value that an ideally rational agent places on a gamble determined by the values that she places on its possible outcomes, together with their mode of composition into the gamble (i.e. the probabilities (...)
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  33. Rationality and indeterminate probabilities.Alan Hájek & Michael Smithson - 2012 - Synthese 187 (1):33-48.
    We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our (...)
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  34. The Bounded Strength of Weak Expectations.J. Sprenger & R. Heesen - 2011 - Mind 120 (479):819-832.
    The rational price of the Pasadena and Altadena games, introduced by Nover and Hájek (2004 ), has been the subject of considerable discussion. Easwaran (2008 ) has suggested that weak expectations — the value to which the average payoffs converge in probability — can give the rational price of such games. We argue against the normative force of weak expectations in the standard framework. Furthermore, we propose to replace this framework by a bounded utility perspective: this shift renders the problem (...)
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  35. Binding and its consequences.Christopher J. G. Meacham - 2010 - Philosophical Studies 149 (1):49-71.
    In “Bayesianism, Infinite Decisions, and Binding”, Arntzenius et al. (Mind 113:251–283, 2004 ) present cases in which agents who cannot bind themselves are driven by standard decision theory to choose sequences of actions with disastrous consequences. They defend standard decision theory by arguing that if a decision rule leads agents to disaster only when they cannot bind themselves, this should not be taken to be a mark against the decision rule. I show that this claim has surprising implications for a (...)
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  36. Preference for equivalent random variables: A price for unbounded utilities.Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane - 2009 - Journal of Mathematical Economics 45:329-340.
    When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference and the status quo, (...)
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  37. Relative Expectation Theory.Mark Colyvan - 2008 - Journal of Philosophy 105 (1):37-44.
    Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. (...)
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  38. Some Remarks on the Ranking of Infinite Utility Streams.Bhaskar Dutta - 2008 - In Kaushik Basu & Ravi Kanbur (eds.), Arguments for a Better World: Essays in Honor of Amartya Sen: Volume I: Ethics, Welfare, and Measurement and Volume Ii: Society, Institutions, and Development. Oxford University Press.
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  39. Strong and weak expectations.Kenny Easwaran - 2008 - Mind 117 (467):633-641.
    Fine has shown that assigning any value to the Pasadena game is consistent with a certain standard set of axioms for decision theory. However, I suggest that it might be reasonable to believe that the value of an individual game is constrained by the long-run payout of repeated plays of the game. Although there is no value that repeated plays of the Pasadena game converges to in the standard strong sense, I show that there is a weaker sort of convergence (...)
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  40. Evaluating the pasadena, altadena, and st petersburg gambles.Terrence L. Fine - 2008 - Mind 117 (467):613-632.
    By recourse to the fundamentals of preference orderings and their numerical representations through linear utility, we address certain questions raised in Nover and Hájek 2004, Hájek and Nover 2006, and Colyvan 2006. In brief, the Pasadena and Altadena games are well-defined and can be assigned any finite utility values while remaining consistent with preferences between those games having well-defined finite expected value. This is also true for the St Petersburg game. Furthermore, the dominance claimed for the Altadena game over the (...)
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  41. Complex Expectations.Alan Hájek & Harris Nover - 2008 - Mind 117 (467):643 - 664.
    In our 2004, we introduced two games in the spirit of the St Petersburg game, the Pasadena and Altadena games. As these latter games lack an expectation, we argued that they pose a paradox for decision theory. Terrence Fine has shown that any finite valuations for the Pasadena, Altadena, and St Petersburg games are consistent with the standard decision-theoretic axioms. In particular, one can value the Pasadena game above the other two, a result that conflicts with both our intuitions and (...)
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  42. Putting expectations in order.Alan Baker - 2007 - Philosophy of Science 74 (5):692-700.
    In their paper, “Vexing Expectations,” Nover and Hájek (2004) present an allegedly paradoxical betting scenario which they call the Pasadena Game (PG). They argue that the silence of standard decision theory concerning the value of playing PG poses a serious problem. This paper provides a threefold response. First, I argue that the real problem is not that decision theory is “silent” concerning PG, but that it delivers multiple conflicting verdicts. Second, I offer a diagnosis of the problem based on the (...)
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  43. Taking Stock of Infinite Value: Pascal’s Wager and Relative Utilities.Paul Bartha - 2007 - Synthese 154 (1):5-52.
    Among recent objections to Pascal's Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek has shown that reformulations of Pascal's Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. Both the objections (...)
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  44. No expectations.Mark Colyvan - 2006 - Mind 115 (459):695-702.
    The Pasadena paradox presents a serious challenge for decision theory. The paradox arises from a game that has well-defined probabilities and utilities for each outcome, yet, apparently, does not have a well-defined expectation. In this paper, I argue that this paradox highlights a limitation of standard decision theory. This limitation can be (largely) overcome by embracing dominance reasoning and, in particular, by recognising that dominance reasoning can deliver the correct results in situations where standard decision theory fails. This, in turn, (...)
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  45. In Memory of Richard Jeffrey: Some Reminiscences and Some Reflections on The Logic of Decision.Alan Hájek - 2006 - Philosophy of Science 73 (5):947-958.
    This paper is partly a tribute to Richard Jeffrey, partly a reflection on some of his writings, The Logic of Decision in particular. I begin with a brief biography and some fond reminiscences of Dick. I turn to some of the key tenets of his version of Bayesianism. All of these tenets are deployed in my discussion of his response to the St. Petersburg paradox, a notorious problem for decision theory that involves a game of infinite expectation. Prompted by that (...)
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  46. Perplexing expectations.Alan Hájek & Harris Nover - 2006 - Mind 115 (459):703 - 720.
    This paper revisits the Pasadena game (Nover and Háyek 2004), a St Petersburg-like game whose expectation is undefined. We discuss serveral respects in which the Pasadena game is even more troublesome for decision theory than the St Petersburg game. Colyvan (2006) argues that the decision problem of whether or not to play the Pasadena game is ‘ill-posed’. He goes on to advocate a ‘pluralism’ regarding decision rules, which embraces dominance reasoning as well as maximizing expected utility. We rebut Colyvan’s argument, (...)
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  47. The two-envelope paradox: An axiomatic approach.Franz Dietrich & Christian List - 2005 - 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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  48. Bayesianism, Infinite Decisions, and Binding.Frank Arntzenius, Adam Elga & John Hawthorne - 2004 - 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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  49. Infinite Archives.David F. Bell - 2004 - Substance 33 (3):148-161.
  50. Infinite utilitarianism: More is always better.Luc Lauwers & Peter Vallentyne - 2004 - Economics and Philosophy 20 (2):307-330.
    We address the question of how finitely additive moral value theories (such as utilitarianism) should rank worlds when there are an infinite number of locations of value (people, times, etc.). In the finite case, finitely additive theories satisfy both Weak Pareto and a strong anonymity condition. In the infinite case, however, these two conditions are incompatible, and thus a question arises as to which of these two conditions should be rejected. In a recent contribution, Hamkins and Montero (2000) have argued (...)
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