Newcomb's Problem

This dissertation primarily consists of three related, published articles on decision theory. All three articles are at least in part a response to various problems and issues raised by an approach known as "causal decision theory". But "Rationality, Group Choice and Expected Utility" goes beyond the issue of causal versus non-causal decision theory, and deals in general with the subject of analysing rational choice in terms of expected utility. I develop a new way of handling cases of rational cooperation within (...) the framework of a straight-forward expected utility analysis. This new approach is employed to resolve The Prisoners' Dilemma and other paradoxical cases of group choice. Both "Counterfactuals and Newcomb's Paradox" and "Rationality Revisited" challenge the claim that causal decision theory adequately captures our notion of rational choice. In particular, both articles take issue with the causal theorist's approach to the infamous Newcomb's Paradox, since that is generally regarded as a pivotal case. It is important to note that the two articles individually provide quite independent arguments for the claim that non-causal decision theorists should not be persuaded by the causal theorist's account of Newcomb's Paradox. Both "Rationality, Group Choice and Expected Utility" and "Rationality Revisited" develop the surprising finding that there is a clear sense in which it is not necessarily true that rationality requires an agent to choose the option that he can determine to have the highest payoff. It is the failure to realize this that leads one astray in Newcomb's Paradox. (shrink)

A standard argument for one-boxing in Newcomb’s Problem is ‘Why Ain’cha Rich?’, which emphasizes that one-boxers typically make a million dollars compared to the thousand dollars that two-boxers can expect. A standard reply is the ‘opportunity defence’: the two-boxers who made a thousand never had an opportunity to make more. The paper argues that the opportunity defence is unavailable to anyone who grants that in another case—a Frankfurt case—the agent is deprived of opportunities in the way that advocates of Frankfurt (...) cases typically claim. (shrink)

The paper discusses Ian Wells’s recent argument that there is a decision problem in which followers of Evidential Decision Theory end up poorer than followers of Causal Decision Theory despite having the same opportunities for money. It defends Evidential Decision Theory against Wells’s argument, on the following grounds. Wells's has not presented a decision problem in which his main claim is true. Four possible decision problems can be generated from his central example, in each of which followers of Evidential Decision (...) Theory do at least as well as followers of Causal Decision Theory. There is another case in which followers of Causal Decision Theory have the same opportunities for making money but end up worse than followers of Evidential Decision Theory. (shrink)

This paper argues that evidential decision theory is incompatible with options having objective values.

According to orthodox causal decision theory, performing an action can give you information about factors outside of your control, but you should not take this information into account when deciding what to do. Causal decision theorists caution against an irrational policy of 'managing the news'. But, by providing information about factors outside of your control, performing an act can give you two, importantly different, kinds of good news. It can tell you that the world in which you find yourself is (...) good in ways you can't control, and it can also tell you that the act itself is in a position to make the world better. While the first kind of news does not speak in favor of performing an act, I believe that the second kind of news does. I present a revision of causal decision theory which advises you to manage the news about the good you stand to promote, while ignoring news about the good the world has provided for you. (shrink)

We argue that causal decision theory is no worse off than evidential decision theory in handling entanglement, regardless of one’s preferred interpretation of quantum mechanics. In recent works, Ahmed and Ahmed and Caulton : 4315–4352, 2014) have claimed the opposite; we argue that they are mistaken. Bell-type experiments are not instances of Newcomb problems, so CDT and EDT do not diverge in their recommendations. We highlight the fact that a Causal Decision Theorist should take all lawlike correlations into account, including (...) potentially acausal entanglement correlations. This paper also provides a brief introduction to CDT with a motivating “small” Newcomb problem. The main point of our argument is that quantum theory does not provide grounds for favouring EDT over CDT. (shrink)

Newcomb’s Problem, Arif Ahmed (editor). Cambridge University Press, 2018, 233 pages.

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 (...) independent. From the former point of view, we show that the probability premisses are not independent but inconsistent, and their inconsistency is provable within probability theory alone. From the latter point of view, we show that their consistency can be saved, but then the contradictory recommendations evaporate. Consequently, whether one subscribes to evidential or causal decision theory, rational decision theory is not in any way vitiated by Rescher’s arguments. (shrink)

I present a decision problem in which orthodox causal decision theory appears to violate weak versions of the independence of irrelevant alternatives (IIA) and normal-form extensive-form equivalence (NEE). I show that these violations lead to exploitable behavior and long-run poverty. These consequences appear damning, but I urge caution. Causalists can dispute the charge that they violate IIA and NEE in this case by carefully specifying when two options in different decision problems are similar enough to be counted as the same.

The more you think about it, the more baffling Newcomb's Problem becomes. To most people, at first it is obvious which solution is correct, but their confidence can be eroded easily. Only a puzzled few are torn between the two right from the start, and for years so was I. But at last, thanks to a certain metaargument, one solution came to seem obvious to me. And yet, imagining myself actually faced with Newcomb's choice, I started to worry that I (...) might experience just enough last-minute ambivalence to unsettle my confidence in that argument. Fortunately, I have found a strategy to ensure making the right choice when the chips are down.Not only is Newcomb's Problem puzzling in its own right, it is philosophically significant. The appeal of both solutions reflects a conflict between two plausible conceptions of rational choice. In making a decision, should one consider all of its probabilistic consequences or only its causal consequences? Each conception has its supporters, but some philosophers find them both defensible and see no hope of resolving the conflict. I think the conflict can be resolved, at least in the context of Newcomb's Problem, by properly assessing the relevant counterfactual conditionals. (shrink)

Until recently, many philosophers took Causal Decision Theory to be more successful than its rival, Evidential Decision Theory. Things have changed, however, with a renewed concern that cases involving an extreme form of decision instability are counterexamples to CDT :392–403, 1984; Egan in Philos Rev 116:93–114, 2007). Most prominent among those cases of extreme decision instability is the Psychopath Button, due to Andy Egan; in that case, CDT recommends a seemingly absurd act that almost certainly results in your death. This (...) renewed attention to decision instability has spurned an array of modifications to and rejections of CDT. I argue, however, that the Psychopath Button and its ilk are no counterexamples to CDT. That is, given the causalist’s commitments in Newcomb Problems, they already have the tools to justify CDT’s verdict in Egan-style cases of extreme decision instability. I first argue that there is no reason to think the Psychopath Button is a counterexample to CDT; in particular, many philosophers have placed too much weight on pre-theoretic intuition in Egan-cases, and apart from pre-theoretic intuition, arguments against CDT in cases of extreme decision instability are flawed. My second claim is that the causalist can provide good reasons for following CDT in cases of extreme decision instability. I present a new case, the Two Button Defense, that highlights precisely why the causalist can reasonably follow CDT in even the Psychopath Button. CDT therefore stands as a viable decision theory, without need for modification, restriction, or rejection. (shrink)

A one-boxer, Erica, and a two-boxer, Chloe, engage in a familiar debate. The debate begins with Erica asking Chloe: ‘If you’re so smart, then why ain’cha rich?’. As the debate progresses, Chloe is led to endorse a novel causalist theory of rational choice. This new theory allows Chloe to forge a connection between rational choice and long-run riches. In brief: Chloe concludes that it is not long-run wealth but rather long-run wealth creation which is symptomatic of rationality.

Historically, the hypothesis that our world is a computer simulation has struck many as just another improbable-but-possible “skeptical hypothesis” about the nature of reality. Recently, however, the simulation hypothesis has received significant attention from philosophers, physicists, and the popular press. This is due to the discovery of an epistemic dependency: If we believe that our civilization will one day run many simulations concerning its ancestry, then we should believe that we are probably in an ancestor simulation right now. This essay (...) examines a troubling but underexplored feature of the ancestor-simulation hypothesis: the termination risk posed by both ancestor-simulation technology and experimental probes into whether our world is an ancestor simulation. This essay evaluates the termination risk by using extrapolations from current computing practices and simulation technology. The conclusions, while provisional, have great implications for debates concerning the fundamental nature of reality and the safety of contemporary physics. (shrink)

The standard formulation of Newcomb's problem compares evidential and causal conceptions of expected utility, with those maximizing evidential expected utility tending to end up far richer. Thus, in a world in which agents face Newcomb problems, the evidential decision theorist might ask the causal decision theorist: "if you're so smart, why ain’cha rich?” Ultimately, however, the expected riches of evidential decision theorists in Newcomb problems do not vindicate their theory, because their success does not generalize. Consider a theory that allows (...) the agents who employ it to end up rich in worlds containing Newcomb problems and continues to outperform in other cases. This type of theory, which I call a “success-first” decision theory, is motivated by the desire to draw a tighter connection between rationality and success, rather than to support any particular account of expected utility. The primary aim of this paper is to provide a comprehensive justification of success-first decision theories as accounts of rational decision. I locate this justification in an experimental approach to decision theory supported by the aims of methodological naturalism. (shrink)

Counter-intuitive consequences of both causal decision theory and evidential decision theory are dramatized. Each of those theories is thereby put under some pressure to supply an error theory to explain away intuitions that seem to favour the other. Because trouble is stirred up for both sides, complacency about Newcomb’s problem is discouraged.

Suppose that you have to take a test tomorrow but you do not want to study. Unfortunately you should study, since you care about passing and you expect to pass only if you study. Is there anything you can do to make it the case that you should not study? Is there any way for you to ‘rationalize’ slacking off? I suggest that such rationalization is impossible. Then I show that if evidential decision theory is true, rationalization is not only (...) possible but sometimes advisable. (shrink)

The 'Why ain'cha rich?' argument for one-boxing in Newcomb's problem allegedly vindicates evidential decision theory and undermines causal decision theory. But there is a good response to the argument on behalf of causal decision theory. I develop this response. Then I pose a new problem and use it to give a new 'Why ain'cha rich?' argument. Unlike the old argument, the new argument targets evidential decision theory. And unlike the old argument, the new argument is sound.

The crucial premise of the standard argument for two-boxing in Newcomb's problem, a causal dominance principle, is false. We present some counterexamples. We then offer a metaethical explanation for why the counterexamples arise. Our explanation reveals a new and superior argument for two-boxing, one that eschews the causal dominance principle in favor of a principle linking rational choice to guidance and actual value maximization.

In a decision making context, an agent’s uncertainty can be either epistemic, i.e. due to her lack of knowledge, or agentive, i.e. due to her not having made use of her decision-making power. In cases when it is unclear whether or not a decision maker presently has control over her own future actions, it is difficult to determine whether her uncertainty is epistemic or agentive. Such situations are often difficult for the agent to deal with, but from an outsider’s perspective, (...) they can have sensible pragmatic solutions. (shrink)

Causal Decision Theory reckons the choice-worthiness of an option to be completely independent of its evidential bearing on its non-effects. But after one has made a choice this bearing is relevant to future decisions. Therefore it is possible to construct problems of sequential choice in which Causal Decision Theory makes a guaranteed loss. So Causal Decision Theory is wrong. The source of the problem is the idea that agents have a special perspective on their own contemplated actions, from which evidential (...) connections that observers can see are either irrelevant or invisible. (shrink)

Newcomb's Problem is a controversial paradox of decision theory. It is easily explained and easily understood, and there is a strong chance that most of us have actually faced it in some form or other. And yet it has proven as thorny and intractable a puzzle as much older and better-known philosophical problems of consciousness, scepticism and fatalism. It brings into very sharp and focused disagreement several long-standing philosophical theories on practical rationality, on the nature of free will, and on (...) the direction and analysis of causation. This volume introduces readers to the nature of Newcomb's Problem, and ten chapters by leading scholars present the most recent debates around the Problem and analyse its ramifications for decision theory, metaphysics, philosophical psychology and political science. Their chapters highlight the status of Newcomb's Problem as a live and continuing issue in modern philosophy. (shrink)

Causalists and Evidentialists can agree about the right course of action in an (apparent) Newcomb problem, if the causal facts are not as initially they seem. If declining $1,000 causes the Predictor to have placed $1m in the opaque box, CDT agrees with EDT that one-boxing is rational. This creates a difficulty for Causalists. We explain the problem with reference to Dummett's work on backward causation and Lewis's on chance and crystal balls. We show that the possibility that the causal (...) facts might be properly judged to be non-standard in Newcomb problems leads to a dilemma for Causalism. One horn embraces a subjectivist understanding of causation, in a sense analogous to Lewis's own subjectivist conception of objective chance. In this case the analogy with chance reveals a terminological choice point, such that either (i) CDT is completely reconciled with EDT, or (ii) EDT takes precedence in the cases in which the two theories give different recommendations. The other horn of the dilemma rejects subjectivism, but now the analogy with chance suggests that it is simply mysterious why causation so construed should constrain rational action. (shrink)

The dominance conditional 'If I drink the contents of cup A, I will drink more than if drink the contents of cup B' is true if we know that the first cup contains more than the second. In the first part of the paper, I show that only one kind of theory of indicative conditionals can explain this fact — a Stalnaker-type semantics. In the second part of the paper, I show that dominance conditionals can help explain a long-standing mystery: (...) the question of how one-boxers and two-boxers are guided by conditionals to their respective answers to the Newcomb problem. I will suggest that both implicitly appeal to a decision theoretic principle I will call the Dominance Norm (DN), a principle that connects indicative dominance conditionals with rational courses of action. Finally, I show that DN in combination with a Stalnaker-type theory of indicatives commits us to the two-boxing answer in the Newcomb problem. (shrink)

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. (...) I then tentatively defend an alternative proposal by Joyce, which produces a similar process of dynamic deliberation but for a different reason. (shrink)

In Bermúdez 2013 I argued against David Lewis’s well-known and widely accepted claim that Newcomb’s problem and the prisoner’s dilemma are really notational variants of a single problem. Mark Walker’s paper in this journal takes issue with my argument. In this note I show how Walker’s criticisms are misplaced. The problems with Walker’s argument point to more general and independently interesting conclusions about, first, the relation between deliberation and decision and, second, the differences between the prisoner’s dilemma, which is a (...) strategic choice problem, and Newcomb’s problem, which is a parametric choice problem. (shrink)

Against the contention of David Lewis Philosophy and Public Affairs 8, 235–240, that the Prisoner’s Dilemma is a Newcomb Problem, José Luis Bermúdez Analysis 73, 423–429, has urged that Lewis’s assimilation removes the very outcome scenarios that make the Dilemma so puzzling. I objected that this criticism of Lewis presupposes that the Dilemma is harder to resolve than Newcomb’s Problem, in effect challenging Bermúdez to justify this assumption. In his 2015 he takes up the challenge, arguing that while the former (...) presents a problem of strategic choice the latter is problem of parametric choice. I argue here that appeal to the distinction between these two kinds of choice cannot sustain the rejection of Lewis’s view. (shrink)

A variety of thought experiments suggest that, if the standard picture of practical rationality is correct, then practical rationality is sometimes an obstacle to practical success. For some, this in turn suggests that there is something wrong with the standard picture. In particular, it has been argued that we should revise the standard picture so that practical rationality and practical success emerge as more closely connected than the current picture allows. In this paper, I construct a choice situation—which I refer (...) to as the Newxin puzzle—and discuss its implications in relation to the revisionist approach just described. Using the Newxin puzzle, I argue that the approach leads to a more radically revisionist picture of practical rationality than current debate suggests. (shrink)

Richard Jeffrey long held that decision theory should be formulated without recourse to explicitly causal notions. Newcomb problems stand out as putative counterexamples to this ‘evidential’ decision theory. Jeffrey initially sought to defuse Newcomb problems via recourse to the doctrine of ratificationism, but later came to see this as problematic. We will see that Jeffrey’s worries about ratificationism were not compelling, but that valid ratificationist arguments implicitly presuppose causal decision theory. In later work, Jeffrey argued that Newcomb problems are not (...) decisions at all because agents who face them possess so much evidence about correlations between their actions and states of the world that they are unable to regard their deliberate choices as causes of outcomes, and so cannot see themselves as making free choices. Jeffrey’s reasoning goes wrong because it fails to recognize that an agent’s beliefs about her immediately available acts are so closely tied to the immediate causes of these actions that she can create evidence that outweighs any antecedent correlations between acts and states. Once we recognize that deliberating agents are free to believe what they want about their own actions, it will be clear that Newcomb problems are indeed counterexamples to evidential decision theory. (shrink)

Andy Egan has presented a dilemma for decision theory. As is well known, Newcomb cases appear to undermine the case for evidential decision theory. However, Egan has come up with a new scenario which poses difficulties for causal decision theory. I offer a simple solution to this dilemma in terms of a modified EDT. I propose an epistemological test: take some feature which is relevant to your evaluation of the scenarios under consideration, evidentially correlated with the actions under consideration albeit, (...) causally independent of them. Hold this feature fixed as a hypothesis. The test shows that, in Newcomb cases, EDT would mislead the agent. Where the test shows EDT to be misleading, I propose to use fictive conditional credences in the EDT-formula under the constraint that they are set to equal values. I then discuss Huw Price’s defence of EDT as an alternative to my diagnosis. I argue that my solution also applies if one accepts the main premisses of Price’s argument. I close with applying my solution to Nozick’s original Newcomb problem. (shrink)

This volume brings together Terence Horgan's essays on paradoxes, both published and new. A common theme unifying these essays is that philosophically interesting paradoxes typically resist either easy solutions or solutions that are formally/mathematically highly technical. Another unifying theme is that such paradoxes often have deep-sometimes disturbing-philosophical morals.

I show that accepting Moss’s claim that features of a rational agent’s credence function can constitute knowledge, together with the claim that a rational agent should only act on the basis of reasons that he knows, predicts and explains evidential decision theory’s failure to recommend the right choice for the Newcomb problem. The Newcomb problem can be seen, in light of Moss’s suggestion, as a manifestation of a Gettier case in the domain of choice. This serves as strong evidence for (...) both Moss’s claim and the knowledge-based action approach. (shrink)

Sequel to Armendt 1986, ‘A Foundation for Causal Decision Theory.’ The representation theorem for causal decision theory is slightly revised, with the addition of a new restriction on lotteries and a new axiom (A7). The discussion gives some emphasis to the way in which appropriate K-partitions are characterized by relations found among the agent’s conditional preferences. The intended interpretation of conditional preference is one that embodies a sensitivity to the agent’s causal beliefs.

It is commonly thought, in line with the position defended in an influential paper by David Lewis, that the decision problems faced in the prisoner’s dilemma and the Newcomb situation are essentially the same problem. José Luis Bermúdez has recently attacked the case Lewis makes for this claim. While I think the claim is false, I contend that Bermúdez’s reason for rejecting Lewis’s argument is inadequate, and then outline what I take to be a better reason for doing so.

Defenders of sophisticated evidential decision theory (EDT) have argued (1) that its failure to provide correct recommendations in problems where the agent believes himself asymmetrically fallible in executing his choices is no flaw of the theory, and (2) that causal decision theory gives incorrect recommendations in certain examples unless it is supplemented with an additional metatickle or ratifiability deliberation mechanism. In the first part of this paper, I argue that both positions are incorrect. In the second part of the paper, (...) I show how the agent's preferences involved in standard counterexamples to EDT, such as Newcomb's problem, violate the Jeffrey/Bolker preference axioms, specifically the Impartiality axiom. (shrink)

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 (...) produce a reply to the most serious objections made so far against CDT and against the particular version of CDT I will defend. (shrink)

I consider a familiar argument for two-boxing in Newcomb's Problem and find it defective because it involves a type of divergence from standard Baysian reasoning, which, though sometimes justified, conflicts with the stipulations of the Newcomb scenario. In an appendix, I also find fault with a different argument for two-boxing that has been presented by Graham Priest.

Examples growing out of the Newcomb problem have convinced many people that decision theory should proceed in terms of some kind of causal probability. I endorse this view and define and investigate a variety of causal probability. My definition is related to Skyrms' definition, but proceeds in terms of objective probabilities rather than subjective probabilities and avoids taking causal dependence as a primitive concept.

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 (...) would if I were to one-box’. But such a subjunctively described aim can justify an action only if it can be seen as generating, in conjunction with the agent’s beliefs, an indicatively describable aim which justifies the action. In the case of the Newcomb agent the aim of ’getting more than I would if I were to one-box’ cannot be seen in this way. (shrink)

There are two boxes in front of you and you are asked to choose between taking only box B or taking both box A and box B. Box A contains $ 1,000. Box B will contain either nothing or $ 1,000,000. What B will contain is (or will be) determined by Predictor, who has an excellent track record of predicting your choices. There are two possibilities. Either Predictor has already made his move by predicting your choice and putting a million (...) dollars in B iff he predicted that you will take only B (like in the standard Newcomb problem); or else Predictor has not yet made his move but will wait and observe what box you choose and then put a million dollars in B iff you take only B. In cases like this, Predictor makes his move before the subject roughly half of the time. However, there is a Metapredictor, who has an excellent track record of predicting Predictor’s choices as well as your own. You know all this. Metapredictor informs you of the following truth functional: Either you choose A and B, and Predictor will make his move after you make your choice; or else you choose only B, and Predictor has already made his choice. Now, what do you choose? (shrink)

It is intuitively attractive to think that it makes a difference in Newcomb’s problem whether or not the predictor is infallible, in the sense of being certainly actually correct. This paper argues that that view is irrational and manifests a well-documented cognitive illusion.

Abstract In an engaging and ingenious paper, Irvine (1993) purports to show how the resolution of Braess? paradox can be applied to Newcomb's problem. To accomplish this end, Irvine forges three links. First, he couples Braess? paradox to the Cohen?Kelly queuing paradox. Second, he couples the Cohen?Kelly queuing paradox to the Prisoner's Dilemma (PD). Third, in accord with received literature, he couples the PD to Newcomb's problem itself. Claiming that the linked models are ?structurally identical?, he argues that Braess solves (...) Newcomb's problem. This paper shows that Irvine's linkage depends on structural similarities?rather than identities?between and among the models. The elucidation of functional disanalogies illuminates structural dissimilarities which sever that linkage. I claim that the Cohen?Kelly queuing paradox cloaks a fine structure that decouples it from both Braess? paradox and the PD (Marinoff, 1996a). I further assert that the putative reduction of the PD to a Newcomb problem (e.g. Brams, 1975; Lewis, 1979) is seriously flawed. It follows that Braess? paradox does not solve Newcomb's problem via the foregoing and herein sundered chain. I conclude by substantiating a stronger claim, namely that Braess'paradox cannot solve Newcomb's problem at all. (shrink)

Probabilistic accounts of causality have long had trouble with ‘spurious’ evidential correlations. Such correlations are also central to the case for causal decision theory—the argument that evidential decision theory is inadequate to cope with certain sorts of decision problem. However, there are now several strong defences of the evidential theory. Here I present what I regard as the best defence, and apply it to the probabilistic approach to causality. I argue that provided a probabilistic theory appeals to the notions of (...) agency and effective strategy, it can avoid the problem of spurious causes. I show that such an appeal has other advantages; and argue that it is not illegitimate, even for a causal realist. (shrink)