A causal decision theorist is shown the following argument: 'One-boxers walk away with $1,000,000 nearly every time; two-boxers walk away with $1,000 nearly every time. Therefore you should one-box.' How does the causal decision theorist respond?
AThe argument is valid — expected value calculations are the correct basis for rational choice
BThe correlation between one-boxing and the large prize is spurious, caused by the predictor's method, not by the player's choice
CAt the moment of your choice, the contents of the opaque box are already fixed — taking both boxes always yields $1,000 more than taking one, regardless of what is in it
DThe argument would be valid only if the predictor's accuracy were 100%; at 99%, two-boxing has higher expected value
The causal decision theorist's core move is to note that at decision time, the box contents are already set — the predictor acted in the past. Since the content of the opaque box is causally independent of your present choice, taking both boxes dominates: you get whatever is in the opaque box PLUS $1,000. The observed correlation between one-boxing and the $1M is real, but correlation does not establish that your choice causes what's already in the box. This is the causal dominance argument.
Question 2 Multiple Choice
A player reasons: 'I am the kind of person who one-boxes. The predictor is nearly perfect. Therefore the box almost certainly contains $1,000,000.' This reasoning exemplifies:
ACausal decision theory — the player correctly identifies that choosing to one-box causes the $1M to be placed
BEvidential decision theory — the player treats one-boxing as strong evidence that the box contains $1M, regardless of whether the choice causally affects the contents
CA logical fallacy — past correlations among other players cannot predict what is in this player's box
DBayesian updating — the player correctly calculates a posterior probability conditional on the predictor's past accuracy
Evidential decision theory (EDT) recommends the action that is best correlated with good outcomes, using conditional expected value: E[outcome | one-box] ≈ $1,000,000 × 0.99 = $990,000 vs. E[outcome | two-box] ≈ $1,000 × 0.99 = ~$1,000. EDT one-boxes. This contrasts with causal decision theory (CDT), which conditions on the causal structure: since your choice does not cause what is already in the box, CDT two-boxes. The disagreement is genuine — neither framework is obviously wrong.
Question 3 True / False
The two-boxing argument in Newcomb's problem rests on the observation that, at the moment of choice, the contents of the opaque box are already determined and cannot be causally changed by your decision.
TTrue
FFalse
Answer: True
This is the exact foundation of the causal dominance argument. Whatever the opaque box contains — $0 or $1,000,000 — taking both boxes yields $1,000 more than taking only the opaque box. If the contents are fixed, two-boxing weakly dominates one-boxing. The causal decision theorist accepts this and two-boxes. The evidential decision theorist rejects this reasoning by focusing on the correlation rather than the causal structure.
Question 4 True / False
Newcomb's problem has a single correct answer — one-boxing — because the expected monetary value of one-boxing ($990,000) clearly exceeds the expected value of two-boxing (~$11,000) given the predictor's 99% accuracy.
TTrue
FFalse
Answer: False
This is the most common misconception: treating evidential expected value as the uniquely correct decision criterion. Causal decision theory also has a coherent expected-value calculation — it conditions on the causal structure and finds that two-boxing always yields $1,000 more. Newcomb's problem has no universally accepted solution precisely because both arguments are internally valid under their respective frameworks. The problem's value is diagnostic: it reveals that causal and evidential decision theories can recommend different actions, forcing us to decide which framework is correct.
Question 5 Short Answer
Why doesn't Newcomb's problem have a universally accepted correct answer, and what makes it philosophically valuable despite this?
Think about your answer, then reveal below.
Model answer: The problem has no consensus answer because two internally coherent decision theories — causal decision theory and evidential decision theory — give opposite recommendations. CDT says two-box (the contents are fixed; dominance reasoning applies). EDT says one-box (the choice is evidentially correlated with the $1M prize). Neither can be dismissed as simply wrong. The philosophical value lies precisely in this impasse: Newcomb's problem serves as a diagnostic that separates the theories, revealing that our intuitions about rational choice are inconsistent. It forces explicit commitment to a framework rather than allowing vague appeals to 'rationality.'
Note also that the problem is not about free will or determinism — it arises even for libertarian free will, since the predictor is empirically accurate rather than metaphysically certain. The predictor need not 'see the future'; it may simply model your decision-making process better than you do. This is what makes the problem unsettling and durable.