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Counterfactuals and Two Kinds of Expected Utility

In A. Hooker, J. J. Leach & E. F. McClennen (eds.), Foundations and Applications of Decision Theory: Vol.II: Epistemic and Social Applications. D. Reidel. pp. 125-162 (1978)

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  1. Richness and rationality: causal decision theory and the WAR argument.Adam Bales - 2018 - Synthese 195 (1):259-267.
    Causal decision theory is one of our most prominent theories of rational choice and the “why ain’cha rich?” argument is one of the most prominent objections to this theory. According to WAR, CDT is not an adequate theory of rational choice because it leads agents to make decisions that foreseeably leave them less well off than agents that decide in some other manner. Some philosophers take WAR to decisively undermine CDT. On the other hand, others take WAR to fail to (...)
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  • Evil and God's Toxin Puzzle.John Pittard - 2016 - Noûs 50 (2):88-108.
    I show that Kavka's toxin puzzle raises a problem for the “Responsibility Theodicy,” which holds that the reason God typically does not intervene to stop the evil effects of our actions is that such intervention would undermine the possibility of our being significantly responsible for overcoming and averting evil. This prominent theodicy seems to require that God be able to do what the agent in Kavka's toxin story cannot do: stick by a plan to do some action at a future (...)
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  • The No Probabilities For Acts-Principle.Marion Ledwig - 2005 - Synthese 144 (2):171-180.
    One can interpret the No Probabilities for Acts-Principle, namely that any adequate quantitative decision model must in no way contain subjective probabilities for actions in two ways: it can either refer to actions that are performable now and extend into the future or it can refer to actions that are not performable now, but will be in the future. In this paper, I will show that the former is the better interpretation of the principle.
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  • A New Problem with Mixed Decisions, Or: You’ll Regret Reading This Article, But You Still Should.Benjamin Plommer - 2016 - Erkenntnis 81 (2):349-373.
    Andy Egan recently drew attention to a class of decision situations that provide a certain kind of informational feedback, which he claims constitute a counterexample to causal decision theory. Arntzenius and Wallace have sought to vindicate a form of CDT by describing a dynamic process of deliberation that culminates in a “mixed” decision. I show that, for many of the cases in question, this proposal depends on an incorrect way of calculating expected utilities, and argue that it is therefore unsuccessful. (...)
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  • Lewis, David: Nuevo Trabajo para una Teoría de los Universales [Translation] - Parte II.David K. Lewis & Diego Morales - 2015 - Ideas Y Valores 64 (158):247-277.
    Second part of the translation into Spanish of David Lewis' "New Work for a Theory of Universals", corresponding to the last sections of the original paper. || Segunda parte de la traducción al español del trabajo de David Lewis "New Work for a Theory of Universals", correspondiente a últimas secciones del artículo original. Artículo original publicado en: Australasian Journal of Philosophy, Vol. 61, No. 4, Dec. 1983, pp. 343-377.
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  • Lost memories and useless coins: revisiting the absentminded driver.Wolfgang Schwarz - 2015 - Synthese 192 (9):3011-3036.
    The puzzle of the absentminded driver combines an unstable decision problem with a version of the Sleeping Beauty problem. Its analysis depends on the choice between “halfing” and “thirding” as well as that between “evidential” and “causal” decision theory. I show that all four combinations lead to interestingly different solutions, and draw some general lessons about the formulation of causal decision theory, the interpretation of mixed strategies and the connection between rational credence and objective chance.
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  • Two-Boxing is Irrational.Harold W. Noonan - 2015 - Philosophia 43 (2):455-462.
    Philosophers debate whether one-boxing or two-boxing is the rational act in a Newcomb situation. I shall argue that one-boxing is the only rational choice. This is so because there is no intelligible aim by reference to which you can justify the choice of two-boxing over one-boxing once you have come to think that you will two-box. The only aim by which the agent in the Newcomb situation can justify his two-boxing is the subjunctively described aim of ‘getting more than I (...)
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  • Against Counterfactual Miracles.Cian Dorr - 2016 - Philosophical Review 125 (2):241-286.
    This paper considers how counterfactuals should be evaluated on the assumption that determinism is true. I argue against Lewis's influential view that the actual laws of nature would have been false if something had happened that never actually happened, and in favour of the competing view that history would have been different all the way back. I argue that we can do adequate justice to our ordinary practice of relying on a wide range of historical truths in evaluating counterfactuals by (...)
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  • Don't Ask, Look! Linguistic Corpora as a Tool for Conceptual Analysis.Roland Bluhm - 2013 - In Miguel Hoeltje, Thomas Spitzley & Wolfgang Spohn (eds.), Was dürfen wir glauben? Was sollen wir tun? Sektionsbeiträge des achten internationalen Kongresses der Gesellschaft für Analytische Philosophie e.V. DuEPublico. pp. 7-15.
    Ordinary Language Philosophy has largely fallen out of favour, and with it the belief in the primary importance of analyses of ordinary language for philosophical purposes. Still, in their various endeavours, philosophers not only from analytic but also from other backgrounds refer to the use and meaning of terms of interest in ordinary parlance. In doing so, they most commonly appeal to their own linguistic intuitions. Often, the appeal to individual intuitions is supplemented by reference to dictionaries. In recent times, (...)
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  • Triviality Pursuit.Alan Hájek - 2011 - Topoi 30 (1):3-15.
    The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I will (...)
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  • Overdetermination in Intuitive Causal Decision Theory.Esteban Céspedes - 2013 - In Miguel Hoeltje, Thomas Spitzley & Wolfgang Spohn (eds.), Was dürfen wir glauben? Was sollen wir tun? Sektionsbeiträge des achten internationalen Kongresses der Gesellschaft für Analytische Philosophie e.V. DuEPublico.
    Causal decision theory defines a rational action as the one that tends to cause the best outcomes. If we adopt counterfactual or probabilistic theories of causation, then we may face problems in overdetermination cases. Do such problems affect Causal decision theory? The aim of this work is to show that the concept of causation that has been fundamental in all versions of causal decision theory is not the most intuitive one. Since overdetermination poses problems for a counterfactual theory of causation, (...)
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  • 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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  • Causal Decision Theory and the Fixity of the Past.Arif Ahmed - 2014 - British Journal for the Philosophy of Science 65 (4):665-685.
    Causal decision theory (CDT) cares only about the effects of a contemplated act, not its causes. The article constructs a case in which CDT consequently recommends a bet that the agent is certain to lose, rather than a bet that she is certain to win. CDT is plainly giving wrong advice in this case. It therefore stands refuted. 1 The Argument2 The Argument in More Detail2.1 The betting mechanism2.2 Soft determinism2.3 The content of P 2.4 The argument again3 The Descriptive (...)
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  • Causation, Chance, and the Rational Significance of Supernatural Evidence.Huw Price - 2012 - Philosophical Review 121 (4):483-538.
    In “A Subjectivist’s Guide to Objective Chance,” David Lewis says that he is “led to wonder whether anyone but a subjectivist is in a position to understand objective chance.” The present essay aims to motivate this same Lewisean attitude, and a similar degree of modest subjectivism, with respect to objective causation. The essay begins with Newcomb problems, which turn on an apparent tension between two principles of choice: roughly, a principle sensitive to the causal features of the relevant situation, and (...)
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  • Reversing 30 years of discussion: why causal decision theorists should one-box.Wolfgang Spohn - 2012 - Synthese 187 (1):95-122.
    The paper will show how one may rationalize one-boxing in Newcomb's problem and drinking the toxin in the Toxin puzzle within the confines of causal decision theory by ascending to so-called reflexive decision models which reflect how actions are caused by decision situations (beliefs, desires, and intentions) represented by ordinary unreflexive decision models.
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  • Self-Subverting Principles of Choice.Michael Perkins & Donald C. Hubin - 1986 - Canadian Journal of Philosophy 16 (1):1 - 10.
    The thesis that rationality consists in the straight-forward maximization of utility has not lacked critics. Typically, however, detractors reject the Humean picture of rationality upon which it seems based; they seek to emancipate reason from the tyranny of the passions. It is, then, noteworthy when an attack on this thesis comes from ‘within the ranks.’David Gauthier's paper ‘Reason and Maximization’ is just such an attack; and for this reason, among others, it is interesting. It is not successful, though. In defense (...)
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  • Causation and Decision.Arif Ahmed - 2010 - Proceedings of the Aristotelian Society 110 (2pt2):111-131.
    Sophisticated ‘tickle’-style defences of Evidential Decision Theory take your motivational state to screen off your act from any state that is causally independent of it, thus ensuring that EDT and CDT converge. That leads to unacceptable instability in cases in which the correct action is obvious. We need a more liberal conception of what the agent controls. It follows that an ordinary deliberator should sometimes consider the past and not only the future to be subject to her present choice.
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  • A Rationalization of Cooperation in the Iterated Prisoner's Dilemma.Wolfgang Spohn - unknown
    The paper is essentially a short version Spohn "Strategic Rationality" which emphasizes in particular how the ideas developed there may be used to shed new light on the iterated prisoner's dilemma (and on iterated Newcomb's problem).
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  • Strategic Rationality.Wolfgang Spohn - unknown
    The paper argues that the standard decision theoretic account of strategies and their rationality or optimality is much too narrow, that strategies should rather condition future action to future decision situations (a point of view already developed in my Grundlagen der Entscheidungstheorie, sect. 4.4), that practical deliberation must therefore essentially rely on a relation of superiority and inferiority between possible future decision situations, that all this allows to substantially broaden the theory of practical rationality, that a long list of points (...)
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  • Arntzenius on ‘Why ain’cha rich?’.Arif Ahmed & Huw Price - 2012 - Erkenntnis 77 (1):15-30.
    The best-known argument for Evidential Decision Theory (EDT) is the ‘Why ain’cha rich?’ challenge to rival Causal Decision Theory (CDT). The basis for this challenge is that in Newcomb-like situations, acts that conform to EDT may be known in advance to have the better return than acts that conform to CDT. Frank Arntzenius has recently proposed an ingenious counter argument, based on an example in which, he claims, it is predictable in advance that acts that conform to EDT will do (...)
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  • 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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  • Plans And Decisions.John L. Pollock - 2004 - Theory and Decision 57 (2):79-107.
    Counterexamples are constructed for classical decision theory, turning on the fact that actions must often be chosen in groups rather than individually, i.e., the objects of rational choice are plans. It is argued that there is no way to define optimality for plans that makes the finding of optimal plans the desideratum of rational decision-making. An alternative called “locally global planning” is proposed as a replacement for classical decision theory. Decision-making becomes a non-terminating process without a precise target rather than (...)
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  • Slote on rational dilemmas and rational supererogation.Joe Mintoff - 1997 - Erkenntnis 46 (1):111-126.
    The so-called optimising conception of rationality includes (amongst other things) the following two claims: (i) that it is irrational to choose an option if you know there is a better one, and (ii) there are no situations in which an agent, through no practical fault of her own, cannot avoid acting irrationally. As part of his ongoing attempt to explain why we need to go beyond the optimising conception, Michael Slote discusses a number of examples in which it seems that (...)
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  • Epistemic value.William G. Lycan - 1985 - Synthese 64 (2):137 - 164.
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  • Newcomb's problem, prisoners' dilemma, and collective action.S. L. Hurley - 1991 - Synthese 86 (2):173 - 196.
    Among various cases that equally admit of evidentialist reasoning, the supposedly evidentialist solution has varying degrees of intuitive attractiveness. I suggest that cooperative reasoning may account for the appeal of apparently evidentialist behavior in the cases in which it is intuitively attractive, while the inapplicability of cooperative reasoning may account for the unattractiveness of evidentialist behaviour in other cases. A collective causal power with respect to agreed outcomes, not evidentialist reasoning, makes cooperation attractive in the Prisoners' Dilemma. And a natural (...)
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  • Mixed strategies and ratifiability in causal decision theory.William Harper - 1986 - Erkenntnis 24 (1):25 - 36.
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  • Some counterexamples to causal decision theory.Andy Egan - 2007 - Philosophical Review 116 (1):93-114.
    Many philosophers (myself included) have been converted to causal decision theory by something like the following line of argument: Evidential decision theory endorses irrational courses of action in a range of examples, and endorses “an irrational policy of managing the news”. These are fatal problems for evidential decision theory. Causal decision theory delivers the right results in the troublesome examples, and does not endorse this kind of irrational news-managing. So we should give up evidential decision theory, and be causal decision (...)
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  • A foundation for causal decision theory.Brad Armendt - 1986 - Topoi 5 (1):3-19.
    The primary aim of this paper is the presentation of a foundation for causal decision theory. This is worth doing because causal decision theory (CDT) is philosophically the most adequate rational decision theory now available. I will not defend that claim here by elaborate comparison of the theory with all its competitors, but by providing the foundation. This puts the theory on an equal footing with competitors for which foundations have already been given. It turns out that it will also (...)
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  • Hierarchical maximization of two kinds of expected utility.Paul Weirich - 1988 - Philosophy of Science 55 (4):560-582.
    Causal decision theory produces decision instability in cases such as Death in Damascus where a decision itself provides evidence concerning the utility of options. Several authors have proposed ways of handling this instability. William Harper (1985 and 1986) advances one of the most elegant proposals. He recommends maximizing causal expected utility among the options that are causally ratifiable. Unfortunately, Harper's proposal imposes certain restrictions; for instance, the restriction that mixed strategies are freely available. To obtain a completely general method of (...)
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  • Conditioning and intervening.Christopher Meek & Clark Glymour - 1994 - British Journal for the Philosophy of Science 45 (4):1001-1021.
    We consider the dispute between causal decision theorists and evidential decision theorists over Newcomb-like problems. We introduce a framework relating causation and directed graphs developed by Spirtes et al. (1993) and evaluate several arguments in this context. We argue that much of the debate between the two camps is misplaced; the disputes turn on the distinction between conditioning on an event E as against conditioning on an event I which is an action to bring about E. We give the essential (...)
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  • Gandalf’s solution to the Newcomb problem.Ralph Wedgwood - 2013 - Synthese 190 (14):2643–2675.
    This article proposes a new theory of rational decision, distinct from both causal decision theory (CDT) and evidential decision theory (EDT). First, some intuitive counterexamples to CDT and EDT are presented. Then the motivation for the new theory is given: the correct theory of rational decision will resemble CDT in that it will not be sensitive to any comparisons of absolute levels of value across different states of nature, but only to comparisons of the differences in value between the available (...)
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  • Probabilistic causality and the question of transitivity.Ellery Eells & Elliott Sober - 1983 - Philosophy of Science 50 (1):35-57.
    After clarifying the probabilistic conception of causality suggested by Good (1961-2), Suppes (1970), Cartwright (1979), and Skyrms (1980), we prove a sufficient condition for transitivity of causal chains. The bearing of these considerations on the units of selection problem in evolutionary theory and on the Newcomb paradox in decision theory is then discussed.
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  • The Dr. Psycho Paradox and Newcomb’s Problem.Michael Clark & Nicholas Shackel - 2006 - Erkenntnis 64 (1):85 - 100.
    Nicholas Rescher claims that rational decision theory “may leave us in the lurch”, because there are two apparently acceptable ways of applying “the standard machinery of expected-value analysis” to his Dr. Psycho paradox which recommend contradictory actions. He detects a similar contradiction in Newcomb’s problem. We consider his claims from the point of view of both Bayesian decision theory and causal decision theory. In Dr. Psycho and in Newcomb’s Problem, Rescher has used premisses about probabilities which he assumes to be (...)
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  • No regrets, or: Edith piaf revamps decision theory.Frank Arntzenius - 2008 - Erkenntnis 68 (2):277-297.
    I argue that standard decision theories, namely causal decision theory and evidential decision theory, both are unsatisfactory. I devise a new decision theory, from which, under certain conditions, standard game theory can be derived.
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  • On the Nature and Relationship of Individual and Collective Justification.Simon Graf - 2024 - Dissertation, University of Leeds
    This thesis is an investigation into the nature of epistemic justification. It brings together themes from traditional, individual-centred epistemology, and collective, group-centred epistemology. The first half of the thesis is concerned with the question of whether rationality is epistemically permissive; that is, whether one body of evidence can rationalise more than one doxastic attitude. In chapter 1, I argue that permissive cases are best understood as epistemic standard conflicts. Doing so provides us with a novel understanding of the arbitrariness objection (...)
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  • Evidence, Causality, and Sequential Choice.Gerard Rothfus - forthcoming - Theory and Decision.
    Philosophers’ two favorite accounts of rational choice, Evidential Decision Theory (EDT) and Causal Decision Theory (CDT), each face a number of serious objections. Especially troubling are the recent charges that these theories are dynamically inconsistent. I note here that, under the epistemic assumptions that validate these charges, every decision theory that satisfies a pair of attractive postulates is doomed to a similar fate and then survey various lessons rational choice theorists might opt to draw from this.
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  • On the plurality of counterfactuals.Ben Holguín & Trevor Teitel - manuscript
    Counterfactuals are context-sensitive. However, we argue that various debates and doctrines in metaphysics and the philosophy of science are premised on ignoring the full extent of counterfactual context-sensitivity. Our focus is on the prominent "miracle" versus "no-miracle" debate about counterfactuals under the assumption that our laws of nature are deterministic. But we also discuss doctrines that employ counterfactuals in theories of rational decision, as well as doctrines that explain what it is to be a law of nature in terms of (...)
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  • Instrumental Divergence.J. Dmitri Gallow - 2024 - Philosophical Studies:1-27.
    The thesis of instrumental convergence holds that a wide range of ends have common means: for instance, self preservation, desire preservation, self improvement, and resource acquisition. Bostrom contends that instrumental convergence gives us reason to think that "the default outcome of the creation of machine superintelligence is existential catastrophe". I use the tools of decision theory to investigate whether this thesis is true. I find that, even if intrinsic desires are randomly selected, instrumental rationality induces biases towards certain kinds of (...)
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  • Counterfactual Decision Theory Is Causal Decision Theory.J. Dmitri Gallow - 2024 - Pacific Philosophical Quarterly 105 (1):115-156.
    The role of causation and counterfactuals in causal decision theory is vexed and disputed. Recently, Brian Hedden (2023) argues that we should abandon causal decision theory in favour of an alternative: counterfactual decision theory. I argue that, pace Hedden, counterfactual decision theory is not a competitor to, but rather a version of, causal decision theory – the most popular version by far. I provide textual evidence that the founding fathers of causal decision theory (Stalnaker, Gibbard, Harper, Lewis, Skyrms, Sobel, and (...)
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  • Causal decision theory, context, and determinism.Calum McNamara - 2024 - Philosophy and Phenomenological Research 109 (1):226-260.
    The classic formulation of causal decision theory (CDT) appeals to counterfactuals. It says that you should aim to choose an option that would have a good outcome, were you to choose it. However, this version of CDT faces trouble if the laws of nature are deterministic. After all, the standard theory of counterfactuals says that, if the laws are deterministic, then if anything—including the choice you make—were different in the present, either the laws would be violated or the distant past (...)
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  • (1 other version)Decisions in Dynamic Settings.Paul Weirich - 1986 - PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986 (1):438-449.
    The expected utility of an option for a decision maker is defined with respect to probability and utility functions that represent the decision maker’s beliefs and desires. Therefore, as the decision maker’s beliefs and desires change, the expected utility of an opinion may change. Some options are such that their realizations change beliefs and desires in ways that change the expected utilities of the options. If a decision is made among options that include one or more of these special options, (...)
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  • Modality, expected utility, and hypothesis testing.WooJin Chung & Salvador Mascarenhas - 2023 - Synthese 202 (1):1-40.
    We introduce an expected-value theory of linguistic modality that makes reference to expected utility and a likelihood-based confirmation measure for deontics and epistemics, respectively. The account is a probabilistic semantics for deontics and epistemics, yet it proposes that deontics and epistemics share a common core modal semantics, as in traditional possible-worlds analysis of modality. We argue that this account is not only theoretically advantageous, but also has far-reaching empirical consequences. In particular, we predict modal versions of reasoning fallacies from the (...)
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  • Unbounded Utility.Zachary Goodsell - 2023 - Dissertation, University of Southern California
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  • Unspecific Evidence and Normative Theories of Decision.Rhys Borchert - forthcoming - Episteme:1-23.
    The nature of evidence is a problem for epistemology, but I argue that this problem intersects with normative decision theory in a way that I think is underappreciated. Among some decision theorists, there is a presumption that one can always ignore the nature of evidence while theorizing about principles of rational choice. In slogan form: decision theory only cares about the credences agents actually have, not the credences they should have. I argue against this presumption. In particular, I argue that (...)
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  • Conditional causal decision theory reduces to evidential decision theory.Mostafa Mohajeri - 2024 - Analytic Philosophy 65 (1):93-106.
    Advocates of Causal Decision Theory (CDT) argue that Evidential Decision Theory (EDT) is inadequate because it gives the wrong result in Newcomb problems. Egan (2007) provides a recipe for converting Newcomb problems to counterexamples to CDT, arguing that CDT is inadequate too. Proposed by Edgington (2011), the Conditional Causal Decision Theory (CCDT) is widely taken uncritically in the recent literature as a version of CDT that conforms to the supposedly correct pre-theoretic judgments about the rationality of acts in Newcomb problems (...)
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  • On Choosing how to Choose.Richard Pettigrew - manuscript
    A decision theory is self-recommending if, when you ask it which decision theory you should use, it considers itself to be among the permissible options. I show that many alternatives to expected utility theory are not self-recommending, and I argue that this tells against them.
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  • Decision, causality, and predetermination.Boris Kment - 2023 - Philosophy and Phenomenological Research 107 (3):638-670.
    Evidential decision theory (EDT) says that the choiceworthiness of an option depends on its evidential connections to possible outcomes. Causal decision theory (CDT) holds that it depends on your beliefs about its causal connections. While Newcomb cases support CDT, Arif Ahmed has described examples that support EDT. A new account is needed to get all cases right. I argue that an option A's choiceworthiness is determined by the probability that a good outcome ensues at possible A‐worlds that match actuality in (...)
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  • A plan-based causal decision theory.Gerard J. Rothfus - 2022 - Analysis 82 (2):264-272.
    In ‘An argument against causal decision theory’, Jack Spencer shows that standard formulations of causal decision theory run afoul of his Guaranteed Principle. In the sequential choice problem he employs to make this case, the transgression stems from an awkward discrepancy between how causalists typically value present vs future acts. This note suggests a version of causal decision theory that avoids this incongruity and so respects the Guaranteed Principle in Spencer’s problem. However, this formulation, and hence symmetric appraisal of present (...)
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  • (1 other version)Structural Stability in Causal Decision Theory.Simon M. Huttegger & Greg Lauro - 2020 - Erkenntnis 87 (2):603-621.
    There are decision problems in which rational deliberation fails to result in choosing a pure act. This phenomenon is known as decision instability and has been discussed in the literature on causal decision theory. In this paper we investigate another type of instability, called structural instability in dynamical systems theory. Structural instability indicates that certain qualitative features of the process of rational deliberation are under-determined in a decision situation. We illustrate some of the issues arising from structural instability with a (...)
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  • Actual value in decision theory.Andrew Bacon - 2022 - Analysis 82 (4):617-629.
    Decision theory is founded on the principle that we ought to take the action that has the maximum expected value from among actions we are in a position to take. But prior to the notion of expected value is the notion of the actual value of that action: roughly, a measure of the good outcomes you would in fact procure if you were to take it. Surprisingly many decision theories operate without an analysis of actual value. I offer a definition (...)
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