Experiment #4 · Thought experiment

Newcomb's Problem

Foreknowledge, choice, and rational decision

William Newcomb; popularised by Robert Nozick · 1969 · Decision theory, philosophy of action

First published: Robert Nozick, "Newcomb's Problem and Two Principles of Choice", in *Essays in Honor of Carl G. Hempel* (1969).

A near-infallible predictor has already filled the boxes. Take both, or just the opaque one?

A very reliable predictor — say, with 99% accuracy — has placed $1,000 in transparent box A and either $1,000,000 or nothing in opaque box B. The Predictor put $1,000,000 in B *iff* it predicted you would take only B. You may take both boxes ("two-boxing") or only B ("one-boxing"). Two-boxing dominates (whatever is in B, you do $1,000 better by also taking A) — yet one-boxers walk away with a million on average, two-boxers with a thousand. The split between *evidential* and *causal* decision theory turns on this case, and behind it sit deeper questions about whether human choice is the kind of thing a predictor *could* in principle anticipate.

Formulation

Box A: $1,000 (visible). Box B: $1,000,000 if Predictor predicted "B only", else $0 (sealed). Predictor accuracy ≈99%. Choose: B only, or A+B. Two-boxing has higher expected utility under causal decision theory; one-boxing under evidential.

Compare this experiment

Dimensions Engaged

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Time

Bears on Time · Freedom and Time · Direction: if a reliable predictor exists, the future is fixed enough to be read off in advance — which constrains how libertarian an account of agency can be.

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Observer

Targets Observer · Agency and Observer · Metaphysical Agency. Whether you "should" one-box depends on whether your choice is causally upstream of the Predictor's inference or just evidentially correlated with it — i.e., on whether you are an agent or a predictable event.

Responses — How Schools Engage

Affirms / takes the bait 2

Determinism

Hard determinism takes the Predictor case as a clean illustration: your "choice" was always going to be what it is, and the Predictor read off the antecedent state. One-box, because that is the kind of person the world made you, and you will walk away rich.

Simulation Theory

If the world admits high-fidelity simulation (as on standard simulation hypotheses), Newcomb-style prediction is in-principle straightforward — and the right move is to one-box, because the "you" the Predictor simulated and the "you" who chooses are the same computation.

Denies / rejects the premise 1

Existentialism

The premise that a Predictor can anticipate a genuine choice is incoherent. Authentic choice is precisely what cannot be derived from antecedent state; the thought experiment smuggles in the conclusion it claims to test.

Reframes the question 2

Naturalism

Causal decision theory: take both boxes. Once the Predictor has acted, your choice cannot change what is in B. The correlation between one-boxing and wealth is real but not causal, and a rational agent acts on causal levers.

Pragmatism

The right policy is the one that, if generally adopted, yields the best outcomes — and one-boxers reliably leave with the million. Functional decision theory (Yudkowsky, Soares) formalises this: choose as though you are choosing the policy the Predictor read off.

Holds it inconclusive 1

Analytic Metaphysics / Logical Atomism

The case is a stable boundary between two reasonable theories of rational choice; neither side has definitively dislodged the other. Treat the verdict as theory-relative.