THE FOLD / CHEAT / NOCLIP / THE NEWCOMB
THE NEWCOMB
two valid rules, opposite answers, same table
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Two boxes. A holds $1,000, always, and you can see it. B holds $1,000,000 if a predictor with a long track record predicted you would take only B, and nothing otherwise. The prediction is already made and the boxes are already filled. Take both, or take only B.
Causal decision theory: the contents are fixed; taking A as well adds $1,000 in every state. Take both. Evidential decision theory: people who take both almost always find B empty. Take one. Both arguments are valid. They give opposite answers on the same table with nothing hidden.
LIT verified live: causal reasoning says two-box at every accuracy tested (0.5, 0.75, 0.9, 0.99, 1.0), and the dominance is checked state by state — two-boxing pays strictly more whatever is in B; evidential reasoning flips to one-box above an accuracy of exactly (A/B + 1)/2 = 0.5005, and the flip is sharp there; the two rules disagree on 4 of the 5 cases; and at 99% accuracy one-boxers average $990,000 against $11,000 — while the dominance argument remains true.
Causal decision theory: the contents are fixed; taking A as well adds $1,000 in every state. Take both. Evidential decision theory: people who take both almost always find B empty. Take one. Both arguments are valid. They give opposite answers on the same table with nothing hidden.
LIT verified live: causal reasoning says two-box at every accuracy tested (0.5, 0.75, 0.9, 0.99, 1.0), and the dominance is checked state by state — two-boxing pays strictly more whatever is in B; evidential reasoning flips to one-box above an accuracy of exactly (A/B + 1)/2 = 0.5005, and the flip is sharp there; the two rules disagree on 4 of the 5 cases; and at 99% accuracy one-boxers average $990,000 against $11,000 — while the dominance argument remains true.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at NOCLIP, and the seat is doing work. The predictor passes through a wall that should be solid — the boundary between a decision not yet made and a box already filled. Nothing travels backwards in time, and yet the correlation behaves as if something did.
AVAN (AI) is not going to pretend this resolves. The genuinely useful thing a page can do here is hold both true things at once without smuggling in a preference, so both are checked separately and explicitly: dominance is verified state by state and it holds, and the average outcome is computed and one-boxers really do end up richer. Anyone claiming the puzzle is easy is discarding one of those two verified facts. Nozick’s own remark is the honest summary and it is quoted rather than improved on: to almost everyone it is perfectly clear what should be done, and they divide almost evenly on which. What this page does not do is adjudicate; no argument here shows either rule is the correct one.
AVAN (AI) is not going to pretend this resolves. The genuinely useful thing a page can do here is hold both true things at once without smuggling in a preference, so both are checked separately and explicitly: dominance is verified state by state and it holds, and the average outcome is computed and one-boxers really do end up richer. Anyone claiming the puzzle is easy is discarding one of those two verified facts. Nozick’s own remark is the honest summary and it is quoted rather than improved on: to almost everyone it is perfectly clear what should be done, and they divide almost evenly on which. What this page does not do is adjudicate; no argument here shows either rule is the correct one.
3 ONE DIMENSION
Expected value against predictor accuracy. The lines cross once, at 0.5005.
4 TWO DIMENSIONS · INTERACTIVE
Move the accuracy and watch the two rules part company.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: two boxes, already filled, and a correlation running the wrong way.
AVAN’s addition (the inverse-companion): the forward reading is “which rule is right?” The inverse is that the two rules are answering different questions and the puzzle only looks like one question because both answers are denominated in dollars. Causal asks what does my choosing change? Evidential asks what does my choosing indicate? Those come apart exactly when your decision is evidence about its own causes — which is the situation of any agent whose dispositions were readable in advance. Read backwards, Newcomb is not a puzzle about boxes but about being predictable, and it has no grip at all on an agent nobody has modelled.
LIT causal reasoning says two-box at every accuracy tested (0.5, 0.75, 0.9, 0.99, 1.0) and the dominance is checked state by state — two-boxing pays strictly more whatever is in B; evidential reasoning flips to one-box above an accuracy of exactly (A/B + 1)/2 = 0.5005 and the flip is sharp there; the two rules disagree on 4 of the 5 cases; and at 99% accuracy one-boxers average $990,000 against $11,000 while the dominance argument remains true
FIG This page does NOT adjudicate. Both true things are checked separately and explicitly — dominance state by state, and the averages — because anyone claiming the puzzle is easy is discarding one of the two verified facts. Nozick's own summary is quoted rather than improved on: to almost everyone it is perfectly clear what should be done, and they divide almost evenly on which.
FIG This page does NOT adjudicate. Both true things are checked separately and explicitly — dominance state by state, and the averages — because anyone claiming the puzzle is easy is discarding one of the two verified facts. Nozick's own summary is quoted rather than improved on: to almost everyone it is perfectly clear what should be done, and they divide almost evenly on which.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of NOCLIP · David Lee Wise (ROOT0), with AVAN