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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. Chaos, Add 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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  3. Infinite Aggregation and Risk.Hayden Wilkinson - forthcoming - Australasian Journal of Philosophy:1-20.
    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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  4. 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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  5. 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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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. Pareto Principles in Infinite Ethics.Amanda Askell - 2018 - Dissertation, New York University
    It is possible that the world contains infinitely many agents that have positive and negative levels of well-being. Theories have been developed to ethically rank such worlds based on the well-being levels of the agents in those worlds or other qualitative properties of the worlds in question, such as the distribution of agents across spacetime. In this thesis I argue that such ethical rankings ought to be consistent with the Pareto principle, which says that if two worlds contain the same (...)
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  13. 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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  14. 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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  15. 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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  16. 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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  17. 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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  18. 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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  19. 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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  20. 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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  21. Clark and Shackel on the Two‐Envelope Paradox.Jonathan Weisberg & Christopher Meacham - 2003 - 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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  22. Undecidability in the Spatialized Prisoner's Dilemma.Patrick Grim - 1997 - Theory and Decision 42:53-80.
    n the spatialized Prisoner’s Dilemma, players compete against their immediate neighbors and adopt a neighbor’s strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without opposition, or (...)
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  23. Infinite Utility.James Cain - 1995 - Australasian Journal of Philosophy 73 (3):401 – 404.
    Suppose we wish to decide which of a pair of actions has better consequences in a case in which both actions result in infinite utility. Peter Vallentyne and others have proposed that one action has better consequences than a second if there is a time after which the cumulative utility of the first action always outstrips the cumulative utility of the second. I argue against this principle, in particular I show how cases may arise in which up to any point (...)
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