In Newcomb's problem, a predictor has placed $1M in Box B if it predicted you'd take only Box B, or $0 if it predicted you'd take both. Both boxes are sealed. What does Causal Decision Theory recommend, and why?
ATake only Box B, because the predictor is nearly always right and one-boxing correlates with $1M
BTake both boxes, because your choice now cannot causally affect what the predictor placed in the box earlier
CTake only Box B, because EDT and CDT always agree in well-defined decision problems
DRefuse to choose — Newcomb's problem is logically incoherent and has no correct answer
CDT evaluates actions by their causal consequences: the intervention of choosing both boxes over one box. Since the boxes are already sealed, your current choice cannot travel backward in time to change what the predictor placed inside. Causally, adding Box A to whatever is in Box B is always strictly better — you get $1000 more regardless of Box B's contents. CDT two-boxes precisely because it ignores correlations that don't run through causal mechanisms. This is also why one-boxers (following EDT) statistically walk away richer: the predictor's accuracy means one-boxing is strong evidence that Box B is full.
Question 2 Multiple Choice
In the Smoking Lesion problem, a genetic lesion causes both a desire to smoke and cancer; smoking itself does not cause cancer. What does Evidential Decision Theory recommend, and why is this considered a flaw?
AEDT recommends smoking, because smoking removes evidence of the lesion by showing non-aversion behavior
BEDT recommends not smoking, because observing yourself smoke is evidence that you have the lesion — and thus cancer — even though the smoking didn't cause it
CEDT recommends smoking, because it causally reduces cancer risk by providing a psychological outlet
DEDT and CDT agree in this case: both recommend not smoking because cancer is a bad outcome
EDT recommends the action with the best expected outcome conditional on performing it. Conditionally on smoking, you observe yourself as someone with a desire to smoke — which is evidence of the lesion — raising your expected probability of cancer. EDT therefore recommends not smoking, treating the correlation between smoking and cancer as decision-relevant even though the causal path runs through the lesion, not the cigarette. This is widely considered a failure of EDT: it recommends foregoing a pleasurable activity to 'manage the evidence' about a fait accompli genetic state. The lesion either exists or it doesn't; smoking cannot change it. CDT correctly recommends smoking (or not, based only on taste/cost), recognizing that the causal path to cancer bypasses the choice.
Question 3 True / False
In Newcomb's problem, CDT recommends two-boxing even though one-boxers empirically walk away with more money.
TTrue
FFalse
Answer: True
True, and this is the core tension that makes Newcomb's problem philosophically important. CDT's reasoning is impeccable within its own framework: at the moment of choice, the box contents are fixed, so taking both is causally dominant (it always adds $1000). Yet EDT one-boxers get $1M while CDT two-boxers get at most $1000. Does rationality require us to follow the causal argument even when it leads to worse outcomes? CDT says yes — the decision was already 'over' when the predictor acted. Critics reply that a decision theory that systematically produces worse outcomes for its adherents seems defective. This tension drives much of the research into functional decision theory and related frameworks.
Question 4 True / False
CDT and EDT give different recommendations whenever a decision involves uncertainty about the state of the world.
TTrue
FFalse
Answer: False
False. CDT and EDT agree in the vast majority of decisions, including most decisions involving uncertainty. They diverge specifically in Newcomb-like problems: situations where the agent's choice is correlated with a causally prior state of the world (like the predictor's prediction). In ordinary decisions — choosing an umbrella when it might rain, investing in uncertain stocks — the action doesn't correlate with the prior state of the world in a way that disconnects causal and evidential reasoning. The frameworks produce different verdicts only when there is a correlation between the action and the world state that does not run through a causal mechanism the agent can influence.
Question 5 Short Answer
What structural feature distinguishes Newcomb-like problems — where CDT and EDT diverge — from ordinary decisions where they agree?
Think about your answer, then reveal below.
Model answer: In Newcomb-like problems, the agent's action is correlated with a causally prior state of the world through a mechanism that the action cannot causally influence. In Newcomb's problem, the predictor's earlier placement of money in the box depends on a prediction of the agent's action — so choice and box contents are correlated, but the choice has no causal power over the already-fixed box contents. In ordinary decisions, either no such backward correlation exists, or the action does causally influence the relevant state. When causal and evidential relevance align, CDT and EDT agree; when they come apart — when 'acting as evidence' conflicts with 'acting as a cause' — they give different verdicts.
This is also why FDT (functional decision theory) was developed: it tries to evaluate actions based on the consequences of the decision procedure that produces them, which can sometimes thread the needle between CDT and EDT. The key insight is that being the kind of agent who one-boxes is different from taking a backward-causal action — FDT argues that the predictor predicts your decision procedure, so choosing to one-box is in some sense causally upstream of the predictor's action, even if temporally downstream. Whether this resolves the debate remains contested.