Newcomb's Problem

The setup

There are two boxes in front of you. Box A is transparent and contains $1,000. Box B is opaque. A predictor, with an essentially perfect track record, has already made its prediction and placed money accordingly. If it predicted you would take only Box B, it put $1,000,000 inside. If it predicted you would take both boxes, it left Box B empty.

You can take both boxes or just Box B. The predictor has already acted. The money is either there or it isn't.

What do you do?

Two principles, one collision

Evidential decision theory says: take only Box B. Look at the track record. People who take only Box B almost always walk away with $1M. People who take both boxes almost always walk away with $1,000. The correlation between your choice and the outcome is overwhelming. Take the option that, in virtually every known case, leads to the better outcome.

Causal decision theory says: take both boxes. By the time you're choosing, the money is fixed. Taking both boxes gets you $1,000 more than taking just Box B, regardless of what's in it. If Box B has $1M, you walk away with $1,001,000 instead of $1M. If Box B is empty, you walk away with $1,000 instead of nothing. Causal dominance is clear: two-boxing is always better by exactly $1,000.

The problem is that both arguments are compelling. One-boxers point to the consistent outcomes. Two-boxers point to the logic: you can't affect a decision that's already been made.

Why it hasn't been settled

The disagreement is really about what decision theory is for. Causal decision theorists say rational choice should track what you can cause to happen. Your choice now has no causal power over a box that's already been filled or left empty. Evidential theorists say rational choice should track the evidence your action provides, and a track record this strong is exactly the kind of evidence that should move you.

Neither side is obviously wrong. The debate has generated counterfactual mugging, tickle defenses, and increasingly elaborate variants, all trying to find the case that forces a decisive verdict. So far, none has.

The intuition pump cuts both ways. Two-boxing feels like it's leaving money on the table. One-boxing feels like trying to affect the past. Both feelings are tracking something real.