Newcomb's Problem Research Articles

Reconciling Evidential and Causal Decision Theory

In this paper I study dynamical models of rational deliberation within the context of Newcomb's problem. Such models have been used to argue against the soundness of the "tickle'" defense of evidential decision theory, which is based on the idea that sophisticated decision makers can break correlations between states and acts by introspecting their own beliefs and desires. If correct, this would show that evidential decision theory agrees with the recommendations of causal decision theory. I argue that an adequate understanding of rational deliberation leads to deliberative processes for which this idea works. My proposal is modest, though. Evidential decision theory cannot always be reconciled with causal decision theory along the lines suggested here, but the agreement between the two theories is broader than previously thought.

Confession of a causal decision theorist

Abstract (1) Suppose that you care only about speaking the truth, and are confident that some particular deterministic theory is true. If someone asks you whether that theory is true, are you rationally required to answer ‘yes’? (2) Suppose that you face a problem in which (as in Newcomb's problem) one of your options – call it ‘taking two boxes’ – causally dominates your only other option. Are you rationally required to take two boxes? Those of us attracted to causal decision theory are under pressure to answer ‘yes’ to both questions. However, it has been shown that many existing decision theories are inconsistent with doing so (Ahmed 2014). A simple proof shows that the same goes for an even wider class of theories: all ‘suppositional’ decision theories. The moral is that causal decision theorists must either answer ‘no’ to one of the above questions, or else abandon suppositional decision theories.

Modal Realism is a Newcomb Problem

Some philosophers worry that if modal realism is true, you have no reason to prevent evils. For if you prevent an evil, you’ll have a counterpart somewhere that allows a similar evil. And if you refrain, your counterpart will end up preventing the relevant evil. Either way one evil is prevented and one is allowed. Your act makes no difference. I argue that this is mistaken. If modal realism is true, you are in a variant of Newcomb’s Problem. And if Lewis’ view about Newcomb’s Problem is true, then your act does make a difference and you should prevent the evil.

The philosopher’s paradox: How to make a coherent decision in the Newcomb Problem

We offer a novel argument for one-boxing in Newcomb’s Problem. The intentional states of a rational person are psychologically coherent across time, and rational decisions are made against this backdrop. We compare this coherence constraint with a golf swing, which to be effective must include a follow-through after the ball is in flight. Decisions, like golf swings, are extended processes, and their coherence with other psychological states of a player in the Newcomb scenario links her choice with the way she is predicted in a common cause structure. As a result, the standard argument for two-boxing is mistaken.

Do the EPR correlations pose a problem for causal decision theory?

We argue that causal decision theory (CDT) is no worse off than evidential decision theory (EDT) in handling entanglement, regardless of one’s preferred interpretation of quantum mechanics. In recent works, Ahmed (Evidence, decision, and causality, Cambridge University Press, Cambridge, 2014) and Ahmed and Caulton (Synthese, 191(18): 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.

Why Take Both Boxes?

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.

Newcomb meets Gettier

I show that accepting Moss’s (Philos Rev 122:1–43, 2013) claim that features of a rational agent’s credence function can constitute knowledge, together with the claim (put forward by several philosophers) 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.

Review of Evidence, Decision and Causality

Arif Ahmed, Evidence, Decision and Causality. Cambridge: Cambridge University Press ð2014Þ ,i x1250 pp., $95.00 ðclothÞ. 1. Introduction. Causal and evidential decision theorists disagree on what beliefs one should consult when making a choice. The former hold that a person should consult her beliefs about the causal relationship between her options and the outcomes that might result from them, but the latter think that a person should base her choice on her beliefs about the evidential relationship between her options and their possible outcomes. The difference between causal and evidential decision theory is irrelevant for most practical purposes. However, the two theories give conflicting advice in those ðrare but often realisticÞ choice situations in which good or bad outcomes are evidentially but not causally related to the options an agent is faced with. The so-called Newcomb problem ðNozick 1969Þ is a particularly vivid ðalbeit unrealisticÞ example of where causal and evidential decision theory disagree. Suppose you are faced with two boxes, one of which ðthe ‘transparent’ boxÞ you know contains $1,000, and the other ðthe ‘opaque’ boxÞ might ðbut is not certain toÞ contain $1,000,000. You are given the choice between taking both boxes and just the opaque one. But before you make the choice, you learn that a predictor, who has been incredibly accurate in his past predictions of choices in this type of situation, has put the million in the opaque box just in case he predicted that you will take that box only. What should you choose? Causal decision theory recommends taking both boxes, since nothing you do now will causally affect whether the million is in the opaque box. But evidential decision theory recommends taking only the opaque box, since everyone

Rejoinder to Bermúdez on Lewis, Newcomb’s Problem and the Prisoner’s Dilemma

Against the contention of David Lewis Philosophy and Public Affairs 8(3), 235–240, (1979) that the Prisoner’s Dilemma is a Newcomb Problem, Jose Luis Bermudez Analysis 73, 423–429, (2013) has urged that Lewis’s assimilation removes the very outcome scenarios that make the Dilemma so puzzling. I objected (Walker Philosophia, 42, 841–859, 2014) that this criticism of Lewis presupposes that the Dilemma is harder to resolve than Newcomb’s Problem, in effect challenging Bermudez 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.

Egan and agents: How evidential decision theory can deal with Egan’s dilemma

Andy Egan has presented a dilemma for decision theory. As is well known, Newcomb cases appear to undermine the case for evidential decision theory (EDT). 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 (i) relevant to your evaluation of the scenarios under consideration, (ii) evidentially correlated with the actions under consideration albeit, (iii) 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.

Infallibility in the Newcomb Problem

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 (A) is irrational and (B) manifests a well-documented cognitive illusion.

Epistemic Decision Theory

I explore the prospects for modelling epistemic rationality (in the probabilist setting) via an epistemic decision theory, in a consequentialist spirit. Previous work has focused on cases in which the truth-values of the propositions in which the agent is selecting credences do not depend, either causally or merely evidentially, on the agent�s choice of credences. Relaxing that restriction leads to a proliferation of puzzle cases and theories to deal with them, including epistemic analogues of evidential and causal decision theory, and of the Newcomb Problem and �Psychopath Button� Problem. A variant of causal epistemic decision theory deals well with most cases. However, there is a recalcitrant class of problem cases for which no epistemic decision theory seems able to match our intuitive judgements of epistemic rationality. This lends both precision and credence to the view that there is a fundamental mismatch between epistemic consequentialism and the intuitive notion of epistemic rationality; the implications for understanding the latter are briefly discussed.

Prisoner's dilemma and Newcomb's problem: why Lewis's argument fails

Prisoner's dilemma and Newcomb's problem: why Lewis's argument fails

Narrative and Noncausal Bargaining

Most philosophical accounts of the puzzle of emotional engagement with characters we know to be fictional treat our emotion as static. This essay argues that it's part of the way humans interact with each other as a social species that a highly dynamic form of noncausal willing and noncausal bargaining enters into all our cooperative relationships with each other. Such bargaining can be illuminated by game theory and, in particular, by the version of prisoner's dilemma known as “Newcomb's problem.” Newcomb's problem models some of our most important relationships with each other and also some of the most central aspects of our relationship with narratives whose outcomes we care intensely about even though our caring cannot affect those outcomes. Fictional characters are especially immune to the exercise of a reader's or audience's will, so Newcomb's problem is particularly relevant to the noncausal nature of the bargaining that readers engage in.

Gandalf’s solution to the Newcomb problem

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.

Causation, Decision Theory, and Bell’s Theorem: A Quantum Analogue of the Newcomb Problem

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. 1. Introduction 2. Newcomb’s Probleme 3. Causal Decision Theory 3.1 Regions of causal influence 3.2 Evidential and effective probabilities 4. The parallel with Bell’s theorem 4.1 Consequences of the analogy 4.1.1 The marble boxes game 4.1.2 Mechanism underlying the marble boxes game 4.1.3 The causalist’s decision 4.1.4 The Bell game 5. Communicated versus Non-communicated Predictions 6. Summary and Conclusion

A resource-bounded agent addresses the newcomb problem

In the Newcomb problem, the standard arguments for taking either one box or both boxes adduce what seem to be relevant considerations, but they are not complete arguments, and attempts to complete the arguments rely upon incorrect principles of rational decision making. It is argued that by considering how the predictor is making his prediction, we can generate a more complete argument, and this in turn supports a form of causal decision theory.

Another Attempt to Put Sleeping Beauty to Rest

Sleeping Beauty has become like Newcomb's problem used to be: a puzzle where both intuitions and arguments cluster around two competing responses. In both cases, the real interest is in the frameworks that are constructed to treat the problem: causal vs. evidential decision theory in the case of Newcomb's problem, and different accounts of essentially indexical or self-locating belief in the case of Sleeping Beauty. Many of the arguments about Sleeping Beauty have been carried out in a common framework for representing self-locating belief, with alternative responses agreeing about the presuppositions of that framework. I want to question some of these presuppositions and to set the problem up in a way that is only subtly different from the standard formulation, but different in a way that I think is important.

Faces of generalized permutohedra

The aim of the paper is to calculate face numbers of simple generalized permutohedra, and study their f-, h - and \gamma -vectors. These polytopes include permutohedra, associahedra, graph-associahedra, simple graphic zonotopes, nestohedra, and other interesting polytopes. We give several explicit formulas for h -vectors and \gamma -vectors involving descent statistics. This includes a combinatorial interpretation for \gamma -vectors of a large class of generalized permutohedra which are flag simple polytopes, and confirms for them Gal's conjecture on the nonnegativity of \gamma -vectors. We calculate explicit generating functions and formulae for h -polynomials of various families of graph-associahedra, including those corresponding to all Dynkin diagrams of finite and affine types. We also discuss relations with Narayana numbers and with Simon Newcomb's problem. We give (and conjecture) upper and lower bounds for f-, h -, and \gamma -vectors within several classes of generalized permutohedra. An appendix discusses the equivalence of various notions of deformations of simple polytopes.

Newcomb's Problem and Repeated Prisoners’ Dilemmas

I present a game-theoretic way to understand the situation describing Newcomb's Problem (NP) which helps to explain the intuition of both one-boxers and two-boxers. David Lewis has shown that the NP may be modelled as a Prisoner's Dilemma game (PD) in which ‘cooperating’ corresponds to ‘taking one box’. Adopting relevant results from game theory, this means that one should take just one box if the NP is repeated an indefinite number of times, but both boxes if it is a one-shot game. Causal decision theorists thus give the right answer for the one-shot situation, whereas the one-boxers’ solution applies to the indefinitely iterated case. Because Nozick's set-up of the NP is ambiguous between a one-shot and a repeated game, both of these solutions may appear plausible—depending on whether one conceives of the situation as one-off or repeated. If the players’ aim is to maximize their payoffs, the symmetric structure of the PD implies that the two players will behave alike both when the game is one-shot and when it is played repeatedly. Therefore neither the observed outcome of both players selecting the same strategy (in the PD) nor, correspondingly, the predictor's accurate prediction of this outcome (in the NP) is at all surprising. There is no need for a supernatural predictor to explain the NP phenomena.