Newcomb's Problem

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)

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.

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)

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.

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)

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)

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 a platitude among decision theorists that agents should choose their actions so as to maximize expected value. But exactly how to define expected value is contentious. Evidential decision theory (henceforth EDT), causal decision theory (henceforth CDT), and a theory proposed by Ralph Wedgwood that this essay will call benchmark theory (BT) all advise agents to maximize different types of expected value. Consequently, their verdicts sometimes conflict. In certain famous cases of conflict—medical Newcomb problems—CDT and BT seem to get (...) things right, while EDT seems to get things wrong. In other cases of conflict, including some recent examples suggested by Andy Egan, EDT and BT seem to get things right, while CDT seems to get things wrong. In still other cases, EDT and CDT seems to get things right, while BT gets things wrong. It's no accident, this essay claims, that all three decision theories are subject to counterexamples. Decision rules can be reinterpreted as voting rules, where the voters are the agent's possible future selves. The problematic examples have the structure of voting paradoxes. Just as voting paradoxes show that no voting rule can do everything we want, decision-theoretic paradoxes show that no decision rule can do everything we want. Luckily, the so-called “tickle defense” establishes that EDT, CDT, and BT will do everything we want in a wide range of situations. Most decision situations, this essay argues, are analogues of voting situations in which the voters unanimously adopt the same set of preferences. In such situations, all plausible voting rules and all plausible decision rules agree. (shrink)

This paper aims to make three contributions to decision theory. First there is the hope that it will help to re-establish the legitimacy of the problem, pace various recent analyses provided by Maitzen and Wilson, Slezak and Priest. Second, after pointing out that analyses of the problem have generally relied upon evidence that is conditional on the taking of one particular option, this paper argues that certain assumptions implicit in those analyses are subtly flawed. As a third contribution, the piece (...) aims to draw attention to an important similarity between Newcomb’s problem and the toxin puzzle. In short, both problems illustrate the fact that you can have a reason to intend to φ without having a reason to actually φ. (shrink)

The Newcomb problem is analysed here as a type of common cause problem. In relation to such problems, if you take the dominated option your expected outcome will be good and if you take the dominant option your expected outcome will be not so good. As is explained, however, these arenot conventional conditional expected outcomes but `conditional evidence expected outcomes' and while in the deliberation process, the evidence on which they are based is only hypothetical evidence.Conventional conditional expected outcomes are (...) more sensitive to your current epistemic state in that they are based purely on actual evidence which is available to you during the deliberation process. So although they are conditional on a certain act being performed, they are not based on evidence that you would have only if that act is performed. Moreover, for any given epistemic state during the deliberation process, your conventional conditional expected outcome for the dominant option will be better than that for the dominated option. The principle of dominance is thus in perfect harmony with the conventional conditional expected outcomes. In relation to the Newcomb problem then, the evidence unequivocally supports two-boxing as the rational option. Yet what is advanced here is not simply a two-boxing strategy. To see why, two stages to the problem need to be recognised. The first stage is that which occurs before the information used by the predictor in making his predictions has been gained. The second stage is after this point. Provided that you are still in the first stage, you have an opportunity to influence whether or not the predictor places the $1m in the opaque box. To maximise the probability that it is, you need to commit yourself to one-boxing. (shrink)

1 Background for the Uninitiated RICHMOND CAMPBELL Paradoxes are intrinsically fascinating. They are also distinctively ...

I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations (...) underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics. (shrink)

Certain paradoxes set us reeling endlessly. In surprise examination paradoxes, pupils' reasonings lead them to reel between expecting an examination and expecting none. With Newcomb's puzzle, choosers reel between reasoning in favour of choosing just one box and choosing two. The paradoxes demand an answer to what it is rational to believe or do. Highlighting other reelings and puzzles, this paper shows that the paradoxes should come as no surprise. The paradoxes demand an end to our reasoning when the conditions (...) they set ensure no end. They equivocate between, so to speak, reasoning in heaven and reasoning on earth; and, on the conditions set, not even an infinite god could reach a conclusion. (shrink)

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)

Newcomb’s problem is a decision puzzle whose difficulty and interest stem from the fact that the possible outcomes are probabilistically dependent on, yet causally independent of, the agent’s options. The problem is named for its inventor, the physicist William Newcomb, but first appeared in print in a 1969 paper by Robert Nozick [12]. Closely related to, though less well-known than, the Prisoners’ Dilemma, it has been the subject of intense debate in the philosophical literature. After three decades, the issues remain (...) unresolved. Newcomb’s problem is of genuine importance because it poses a challenge to the theoretical adequacy of orthodox Bayesian decision theory. It has led both to the development of causal decision theory and to efforts aimed at defending the adequacy of the orthodox theory. (shrink)

Doris Olin's Paradox is a very helpful book for those who want to be introduced to the philosophical treatment of paradoxes, or for those who already have knowledge of the general area and would like to have a helpful resource book.

Newcomb's Paradox thus serves as an illustrative vindication of the compatibility of divine foreknowledge and human freedom. A proper understanding of the counterfactual conditionals involved enables us to see that the pastness of God's knowledge serves neither to make God's beliefs counterfactually closed nor to rob us of genuine freedom. It is evident that our decisions determine God's past beliefs about those decisions and do so without invoking an objectionable backward causation. It is also clear that in the context of (...) foreknowledge, backtracking counterfactuals are entirely appropriate and that no alteration of the past occurs. With the justification of the one box strategy, the death of theological fatalism seems ensured. *** DIRECT SUPPORT *** A0985044 00003. (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)

• What’s essential to Newcomb’s problem? 1. You must choose between two particular acts: A1 = you take just the opaque box; A2 = you take both boxes, where the two states of nature are: S 1 = there’s $1M in the opaque box, S2 = there’s $0 in the opaque box.

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)

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.

Should we act only for the sake of what we might bring about (causal decision theory); or is it enough for a decent motive that our action is highly correlated with something desirable (evidential decision theory)? The conflict between these points of view is embodied in Newcomb's problem. It is argued here that intuitive evidence from familiar decision contexts does not enable us to settle the issue, since the two theories dictate the same results in normal circumstances. Nevertheless, there are (...) several reasons to reject the causal approach: (1) its relative complexity; (2) its commitment to the existence of situations in which every possible act would be irrational; (3) its incorporation of an arbitrary time bias; and (4) its implicit distinction between what ought to be done and what ought to be hoped for. (shrink)

In their development of causal decision theory, Allan Gibbard and William Harper advocate a particular method for calculating the expected utility of an action, a method based upon the probabilities of certain counterfactuals. Gibbard and Harper then employ their method to support a two-box solution to Newcomb’s paradox. This paper argues against some of Gibbard and Harper’s key claims concerning the truth-values and probabilities of counterfactuals involved in expected utility calculations, thereby disputing their analysis of Newcomb’s Paradox. If we are (...) right, then Gibbard and Harper’s method of calculating expected utility does not adequately represent rational choice. (shrink)

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 (...) though unwarranted assumption of such a power may account for the intuitive appeal of the one-box response in Newcomb's Problem. (shrink)

Abstract Newcomb's problem is regularly described as a problem arising from equally defensible yet contradictory models of rationality. Braess? paradox is regularly described as nothing more than the existence of non?intuitive (but ultimately non?contradictory) equilibrium points within physical networks of various kinds. Yet it can be shown that Newcomb's problem is structurally identical to Braess? paradox. Both are instances of a well?known result in game theory, namely that equilibria of non?cooperative games are generally Pareto?inefficient. Newcomb's problem is simply a limiting (...) case in which the number of players equals one. Braess? paradox is another limiting case in which the ?players? need not be assumed to be discrete individuals. The result is that Newcomb's problem is no more difficult to solve than (the easy to solve) Braess? paradox. (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)