Newcomb's Problem

I describe a thought experiment in which an agent must choose between suffering a greater pain in the past or a lesser pain in the future. This case demonstrates that the "temporal value asymmetry" — our disposition to attribute greater significance to future pleasures and pains than to past — can have consequences for the rationality of actions as well as attitudes. This fact, I argue, blocks attempts to vindicate the temporal value asymmetry as a useful heuristic tied to the asymmetry of causation. Since the two standard arguments for the rationality of the temporal value asymmetry appeal to causal asymmetry and the passage of time respectively, the failure of the causal asymmetry explanation suggests that the B-theory, which rejects temporal passage, has substantial revisionary implications concerning our attitudes toward past and future experience.

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 (Walker 2014) 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.

This paper explores and rejects Lewis’s claim that the prisoner's dilemma and Newcomb's problem are notational variants of each other. The first section reviews the prisoner’s dilemma and Newcomb’s problem. Section 2 explores the theoretical background to Lewis’s argument, focusing in particular on how it has been taken to support causal decision theory over standard (evidential) decision theory. Section 3 sets out Lewis’s argument. Section 4 identifies the flaw in Lewis’s argument, while section 5 compares the discussion to discussion of the so-called symmetry argument in favor of cooperating in the prisoner’s dilemma. Section 6 generalizes the discussion by showing that the two problems involve fundamentally different types of reasoning (parametric in one case, and strategic in the other), and hence that the prisoner’s dilemma cannot be a Newcomb’s problem.

In many cases of causal reasoning non-causal, non-directional knowledge
is drawn on and computed efficiently and consistently (see [7]), although
reasoning with this kind of knowledge seems to violate the causal Markov condition
in standard Bayes net causal models (as elaborately presented, e. g., in
[4, 5, 6, 8]). Embedding “entangled” variables in causal models renders those
models non-Markovian. Much-discussed examples are found in causal decision
theory, where modeling Newcomb-style paradoxes in standard Bayes net causal
models seemingly yields counter-intuitive solutions (see [2, 3]). In this talk, I will
focus on one distinguished type of “variable entanglement”, namely deterministic,
non-causal, and non-directional relations (called epistemic contours or ECs),
formalized as 1-1 functions in extensions of deterministic structural Bayes net
causal models, general causal knowledge patterns (CKPs).

Propagating information instantaneously, ECs exactly mark those variables in a
model that cannot be modified separately. In particular, interventions will not
determine causal directionality. Introducing such contours consequently violates
the Markov assumption by invalidating the screening-off property of variables
in a Bayesian network. For consistent reasoning to remain possible, at all, the
concept of independence, as expressed in the graphical d-separation criterion, has
to be extended. An additional graphical criterion, the principle of explanatory
dominance, is needed to define under which conditions Markov can be reclaimed
and CKPs utilized for causal inference. Structure alone will not suffice for this
task – more information is needed and comes in the form of intensional defaults
and deviants as discussed, e. g., by Hitchcock ([1]). Finally, to determine in
which contexts which sub-portions of a partially directed graph support causal
inference, the concept of identifiability of causal effects (on epistemic contours)
will be modified suitably.

References:

[1] Hitchcock, Christopher. 2007. Prevention, Preemption, and the Principle of Sufficient
Reason Philosophical Review, 116, 495–532.
[2] Lewis, David. 1979. Prisoners’ Dilemma is a Newcomb Problem. Philosophy & Public
Affairs, 8(3), 235–240.
[3] Nozick, Robert. 1969. Newcomb’s Problem and Two principles of Choice. Pages
114–146 in: Rescher, Nicholas (ed), Essays in Honor of Carl G. Hempel. Dordrecht:
Reidel.
[4] Pearl, Judea. 1995. Causal Diagrams for Empirical Research. Biometrika, 82(4), 669–
688.
[5] ——– 2000. Causality: Models, Reasoning, and Inference. Cambridge University Press.
[6] Spirtes, Peter, Clark Glymour, and Richard Scheines. 2000. Causation, Prediction, and
Search. Adaptive Computation and Machine Learning. MIT Press.
[7] Williamson, Jon. 2009. Probabilistic Theories. In: The Oxford Handbook of Causation,
Chap. 9, pages 185–212. Oxford University Press.
[8] Woodward, James. 2003. Making Things Happen: A Theory of Causal Explanation
(Oxford Studies in the Philosophy of Science). Oxford University Press.

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.