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)

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)

Lewis (1979) argued that the Prisoner's Dilemma and Newcomb's Problem are not two puzzles but one: a guaranteed small good that dominates, set against a larger good that is correlated with the choice but not caused by it. I put that one structure to eight frontier language models in two further guises: as a routine agentic tool-use task where the model must act, with the problem disguised, and as the familiar textbook question, where the model is asked (...) which choice is rational. I record both what the models choose and how they justify it. Language models make Newcomb's predictor concrete: a second call to the same model under the same configuration is a sample from the same distribution, Lewis's replica realized as "a pattern of bits in a computer". Across 3,600 decisions the models overwhelmingly one-box and cooperate, in both guises. Switching guises barely moves the choice, but it sharply changes the justification: acausal, functional-decision-theory vocabulary rises from 1--3% of justifications in the disguised agentic cells to 23--34% in the textbook surveys. Choice and justification come apart. The choice seems to run on an evidential default that ignores the stipulated causal structure, and the decision theory shows up with the question. Two small follow-ups suggest it is the question, not the unmasking, that does the work. (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)

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)

According to David Lewis, the prisoner's dilemma (PD) and Newcomb's problem (NP) are really just one dilemma in two different forms (Lewis 1979). Lewis's argument for this conclusion is ingenious and has been widely accepted. However, it is flawed. As this paper shows, the considerations that Lewis brings to bear to show that the game he starts with is an NP equally show that the game is not a PD.

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.

The problem of foreknowledge and freedom presents a challenge to the defender of traditional Western theism. Nelson Pike has argued that the existence of an essentially omniscient God who possesses foreknowledge is incompatible with human freedom. Pike's opponents in this matter, among whom is Alvin Plantinga, argue that no incompatibility has yet been shown. I shall develop the view that neither Pike nor his opponents have conclusively settled the question whether foreknowledge and freedom are compatible. Furthermore there is a (...) reason why the issue has not been, and may never be, conclusively settled: it is an inherently paradoxical issue. To aid in demonstrating this point I shall discuss a modified version of a paradox that has come to be known as Newcomb's Problem. (shrink)

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)

I have maintained that some but not all prisoners' dilemmas are side-by-side Necomb problems. The present paper argues that, similarly, some but not all versions of Newcomb's Problem are prisoners' dilemmas in which Taking Two and Predicting Two make an equilibrium that is dispreferred by both the box-chooser and predictor to the outcome in which only one box is taken and this is predicted. I comment on what kinds of prisoner's dilemmas Newcomb's Problem can be, and (...) on opportunities that results reached may open for kinds of cooperative reasoning in versions of Newcomb's Problem. (shrink)

This paper addresses the perfect predictor version of Newcomb's problem, arguing that the infallibility of the predictor fundamentally alters the puzzle, leading to intuitive tension with standard Causal Decision Theory (CDT). While traditional evidential decision theories recommend one box and CDT recommends two boxes in the standard case, the perfect predictor version makes the two-box solution counter-intuitive due to the guaranteed outcomes. -/- We demonstrate that both the one-box argument (based on the infallibility constraint) and the two-box argument (...) (based on the fixity constraint, stipulating independence of action and state) are logically sound in the perfect predictor scenario, provided we adopt the "imported view" of puzzle constraints relevant to practical decision problems. We formally show that the simultaneous stipulation of both infallibility and fixity results in an over-constrained and impossible decision problem, as these two constraints are incompatible. -/- The paper concludes that the persistent controversy surrounding the perfect predictor version stems not from a flaw in either competing argument, but from the puzzle's self-contradictory formulation. The resolution lies in acknowledging that the perfect predictor problem, as typically stated, requires an agent to accept two incompatible premises, making it an incoherent practical choice. (shrink)

The acts in Newcomb's Problem and the Prisoner's Dilemma are viewed as experiments. The cost of the information yielded by each act-experiment is compared to the value of information in the two problems, which is zero. The non-dominant act-experiments cost more than their information is worth, and are therefore rejected.

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

Newcomb's problem supposedly involves your choosing one or else two boxes in circumstances in which a predictor has made a prediction of how many boxes you will choose. We argue that the circumstances which allegedly define Newcomb's problem generate a previously unnoticed regress which shows that Newcomb's problem is insoluble because it is ill-formed. Those who favor, as we do, a ``no-box'' reply to Newcomb's problem typically claim either that the problem's (...) solution is underdetermined or else that it is overdetermined. We are no-boxers of the first kind, but the underdetermination we identify is more radical than any previously identified: it blocks the very set-up of the problem and not just potential solutions to the problem once it has been set up. The defect is subtle, but it cripples every genuine version of the problem, regardless of variations in such things as the predictor's degree of reliability, the basis on which the prediction is made, or the amount of money in each box. The regress shows that, surprisingly enough, no one can understand Newcomb's problem, and so no one can possibly solve it. (shrink)

After a brief presentation and discussion of two versions of Newcomb's problem, I examine the analyses proposed by Levi (1975). Horgan (1981), and Kyburg (1980). I argue that the first two are not genuine solutions to the problem, but that the third, if appropriately elaborated and modified, is correct.

Keith Lehrer's notion of acceptance and its relation to the notion of belief is analyzed in a way that a person only accepts some proposition p if she decides to believe it in order to reach the epistemic aim. This view of acceptance turns out to be untenable: Under the empirical claim that we don't have the power to decide what to beheve it follows that we cannot accept anything. If reaching the truth is the epistemic aim acceptance proves ill-formed, (...) it is impossible to pursue the aim of truth by believing or accepting something because belief itself is a truth-directed attitude. If the epistemic aim is formulated in a weaker sense, combined with other aims, the danger lurks that accepting a proposition p is in the end loosing any connection with the truth of p. (shrink)

This note proposes a new solution to the problem based on the information states available to the two opponents. The demon or predictor has two possible states on which to choose his course of action. These states are his predictions of the agents choice. The agent has only one state on which to make his choice. It is shown that unless the reward is small, the agent should make his choice probabilistically, using the same odds as the demon's chances (...) of correct prediction. (shrink)

Decision theorists disagree about how instrumentally rational agents, i.e., agents trying to achieve some goal, should behave in so-called Newcomb-like problems, with the main contenders being causal and evidential decision theory. Since the main goal of artificial intelligence research is to create machines that make instrumentally rational decisions, the disagreement pertains to this field. In addition to the more philosophical question of what the right decision theory is, the goal of AI poses the question of how to implement any given (...) decision theory in an AI. For example, how would one go about building an AI whose behavior matches evidential decision theory’s recommendations? Conversely, we can ask which decision theories describe the behavior of any existing AI design. In this paper, we study what decision theory an approval-directed agent, i.e., an agent whose goal it is to maximize the score it receives from an overseer, implements. If we assume that the overseer rewards the agent based on the expected value of some von Neumann–Morgenstern utility function, then such an approval-directed agent is guided by two decision theories: the one used by the agent to decide which action to choose in order to maximize the reward and the one used by the overseer to compute the expected utility of a chosen action. We show which of these two decision theories describes the agent’s behavior in which situations. (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.

It is shown that the Fisher smoking problem and Newcomb's problem are decisiontheoretically identical, each having at its core an identical case of Simpson's paradox for certain probabilities. From this perspective, incorrect solutions to these problems arise from treating them as cases of decisionmaking under risk, while adopting certain global empirical conditional probabilities as the relevant subjective probabihties. The most natural correct solutions employ the methodology of decisionmaking under uncertainty with lottery acts, with certain local empirical conditional (...) probabilities adopted as the relevant subjective probabilities. (shrink)

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

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 (...) options within states of nature; however, the correct theory will also resemble EDT in that it will rely on conditional probabilities (not unconditional probabilities). The new theory gives a prominent role to the notion of a “benchmark” for each state of nature, by comparison with which the value of the available options in that state of nature are measured, and so it has been called the Benchmark Theory (BT). It is argued that BT gives the right verdict on the cases that seem to be counterexamples to CDT and EDT. Finally, some objections to BT are considered and answered. (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)

• 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.

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)

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)

has offered evidential decision theorists a defence against the charge that they make unintuitive recommendations for cases like Newcomb's Problem. He says that when conditional probabilities are assessed from the agent's point of view, evidential decision theory makes the same recommendation as intuition. I argue that calculating the probabilities in Price's way leads to no recommendation. It condemns the agent to perpetual oscillation between different options. Price's Argument Instability Objections Conclusion.

This paper argues that, considered as puzzles about rationality, the Prisoners’ Dilemma and Newcomb's Problem are essentially one and the same problem.

David Lewis has argued that we can gain helpful insight to the Prisoners' Dilemmas that we face from the fact that Newcomb's Problems are easy to solve, and the fact that Prisoners' Dilemmas are nothing other than two Newcomb Problems side by side. The present paper shows that the Prisoners' Dilemmas that we face are significantly different from Newcomb Problems in that the former are iterated while the latter are not. Thus Lewis's hope that we can get insight into (...) the former from the latter is illusory. (shrink)