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Probabilities Cannot Be Rationally Neglected

Mind 125 (499):759-762 (2016)

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  1. 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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  • Expected choiceworthiness and fanaticism.Calvin Baker - 2024 - Philosophical Studies 181 (5).
    Maximize Expected Choiceworthiness (MEC) is a theory of decision-making under moral uncertainty. It says that we ought to handle moral uncertainty in the way that Expected Value Theory (EVT) handles descriptive uncertainty. MEC inherits from EVT the problem of fanaticism. Roughly, a decision theory is fanatical when it requires our decision-making to be dominated by low-probability, high-payoff options. Proponents of MEC have offered two main lines of response. The first is that MEC should simply import whatever are the best solutions (...)
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  • Against Anti-Fanaticism.Christian Tarsney - manuscript
    Should you be willing to forego any sure good for a tiny probability of a vastly greater good? Fanatics say you should, anti-fanatics say you should not. Anti-fanaticism has great intuitive appeal. But, I argue, these intuitions are untenable, because satisfying them in their full generality is incompatible with three very plausible principles: acyclicity, a minimal dominance principle, and the principle that any outcome can be made better or worse. This argument against anti-fanaticism can be turned into a positive argument (...)
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  • How to Save Pascal (and Ourselves) From the Mugger.Avram Hiller & Ali Hasan - forthcoming - Dialogue:1-17.
    In this article, we re-examine Pascal’s Mugging, and argue that it is a deeper problem than the St. Petersburg paradox. We offer a way out that is consistent with classical decision theory. Specifically, we propose a “many muggers” response analogous to the “many gods” objection to Pascal’s Wager. When a very tiny probability of a great reward becomes a salient outcome of a choice, such as in the offer of the mugger, it can be discounted on the condition that there (...)
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  • A dilemma for Nicolausian discounting.Pietro Cibinel - 2023 - Analysis 83 (4):662-672.
    Orthodox decision theory is fanatical in the way it treats small probabilities of enormous value, if unbounded utility functions are allowed. Some have suggested a fix, Nicolausian discounting, according to which outcomes with small enough probabilities should be ignored when making decisions. However, there are lotteries involving only small-probability outcomes, none of which should intuitively be ignored. So the Nicolausian discounter needs a procedure for distinguishing the problematic cases of small-probability outcomes from the unproblematic ones. In this paper, I present (...)
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  • 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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  • Average Utilitarianism Implies Solipsistic Egoism.Christian J. Tarsney - 2023 - Australasian Journal of Philosophy 101 (1):140-151.
    ABSTRACT Average utilitarianism and several related axiologies, when paired with the standard expectational theory of decision-making under risk and with reasonable empirical credences, can find their practical prescriptions overwhelmingly determined by the minuscule probability that the agent assigns to solipsism—that is, to the hypothesis that there is only one welfare subject in the world, namely, herself. This either (i) constitutes a reductio of these axiologies, (ii) suggests that they require bespoke decision theories, or (iii) furnishes an unexpected argument for ethical (...)
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  • Totalism without Repugnance.Jacob M. Nebel - 2022 - In Jeff McMahan, Timothy Campbell, Ketan Ramakrishnan & Jimmy Goodrich (eds.), Ethics and Existence: The Legacy of Derek Parfit. New York, NY: Oxford University Press. pp. 200-231.
    Totalism is the view that one distribution of well-being is better than another just in case the one contains a greater sum of well-being than the other. Many philosophers, following Parfit, reject totalism on the grounds that it entails the repugnant conclusion: that, for any number of excellent lives, there is some number of lives that are barely worth living whose existence would be better. This paper develops a theory of welfare aggregation—the lexical-threshold view—that allows totalism to avoid the repugnant (...)
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  • How to Avoid Maximizing Expected Utility.Bradley Monton - 2019 - Philosophers' Imprint 19.
    The lesson to be learned from the paradoxical St. Petersburg game and Pascal’s Mugging is that there are situations where expected utility maximizers will needlessly end up poor and on death’s door, and hence we should not be expected utility maximizers. Instead, when it comes to decision-making, for possibilities that have very small probabilities of occurring, we should discount those probabilities down to zero, regardless of the utilities associated with those possibilities.
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  • Absolutism and its Limits.John Hawthorne, Yoaav Isaacs & Clayton Littlejohn - 2023 - Journal of Moral Philosophy 21 (1-2):170-189.
    Many philosophers think that given the choice between saving the life of an innocent person and averting any number of minor ailments or inconveniences, it would be better to save the life. How, then, should one compare the risk of an innocent person’s life to such minor ailments and inconveniences? If lives are infinitely more important than insignificant factors then any risk cannot be outweighed, and that is untenable. An alternative approach seems more promising: let the values of such insignificant (...)
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  • 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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  • Probability discounting and money pumps.Petra Kosonen - forthcoming - Philosophy and Phenomenological Research.
    In response to cases that involve tiny probabilities of huge payoffs, some argue that we ought to discount small probabilities down to zero. However, this paper shows that doing so violates Independence and Continuity, and as a result of these violations, those who discount small probabilities can be exploited by money pumps. Various possible ways of avoiding exploitation will be discussed. This paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities. Much of the discussion (...)
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