Paradox of the Day

One puzzle a day — logical, philosophical, statistical, temporal.

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Newcomb’s Paradox

William Newcomb, popularised by Robert Nozick · 1969

The puzzle

Box A is transparent and contains $1,000. Box B is opaque. A near-perfect predictor has, before your arrival, put $1,000,000 in B if she predicted you would take only B, or left B empty if she predicted you would take both. Take only B, or take both?
Domain
Decision theory
Attribution
William Newcomb, popularised by Robert Nozick
Date
1969

Note

Two arguments collide. Dominance says take both: whatever is in B is already in B; the extra $1,000 is free money. Expected utility says take only B: because the predictor will have predicted you well, the only-B world is overwhelmingly the millionaire one. The thought experiment splits philosophers cleanly down the middle and has done so for fifty years. The problem isn’t computational; it is that two principles we think we hold disagree about which box contains the most money in a world where what you choose retroactively explains what was already true. Causal decision theorists take both boxes; evidential decision theorists take one. Almost no one switches sides after their first reading. Whatever you initially want to do, the paradox is that the other camp is just as smart.

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