It's an objection to Newcomb's specifically, not cause or decision theory generally. My position may be a bit too complex for a comment, but here's the gist.
Newcomb's assumes that deciding A will result in universe X, and deciding B will result in universe Y. It uses the black box of Omega's prediction process to forbid us from calling the connection causal, thus preventing CDT from working, but it requires that our decision be causal, because if it weren't there would be no reason not to two-box. Thus, it assumes causation but prohibits us from calling it causation. If we actually understood how our choosing to pick up the opaque box would result in it being empty, the problem would be entirely trivial. Thus, Newcomb's disproves CDT by assuming causation-that-is-not-causation, and such an assumption does not seem to actually prove anything about the world.
The smoking lesion problem has the same flaw in reverse. It requires EDT to assume that Susan's choice is relevant to whether she gets cancer, but it also assumes that Susan's choice is not relevant to her getting cancer. This linguistic doublethink is all that makes the problem difficult.
In Newcomb's, a full understanding of how Omega's prediction works should make the problem trivial, because it could be incorporated into CDT. If we don't assume that it does work, the problem doesn't work; there's no reason not to use CDT if Omega can't predict systematically. In the Smoking Lesion, a proper understanding of the cocorrelate that actually does cause cancer would make the problem doable in EDT, since it would be obvious that her chance of getting cancer is independent of her choice to smoke. If we don't assume that such a cocorrelate exists the problem doesn't work; EDT says Susan shouldn't smoke, which basically makes sense if the correlation has a meaningful chance of being causal. This is what I mean by it's a linguistic problem; language allows us to express these examples with no apparent contradiction, but the contradiction is there if we break it down far enough.
What if we ran a contest of decision theories on Newcomb's problem in a similar fashion to Axelrod's test of iterated PD programs? I (as Omega) would ask you to submit an explicit deterministic program X that's going to face a gauntlet of simple decision theory problems (including some Newcomb-like problems), and the payoffs it earns will be yours at the end.
In this case, I don't think you'd care (for programming purposes) whether I analyze X mathematically to figure out whether it 1- or 2-boxes, or whether I run simulations of X to see what it does, or a...
(This is the first, and most newcomer-accessible, post in a planned sequence.)
Newcomb's Problem:
Joe walks out onto the square. As he walks, a majestic being flies by Joe's head with a box labeled "brain scanner", drops two boxes on the ground, and departs the scene. A passerby, known to be trustworthy, comes over and explains...
If Joe aims to get the most money, should Joe take one box or two?
What are we asking when we ask what Joe "should" do? It is common to cash out "should" claims as counterfactuals: "If Joe were to one-box, he would make more money". This method of translating "should" questions does seem to capture something of what we mean: we do seem to be asking how much money Joe can expect to make "if he one-boxes" vs. "if he two-boxes". The trouble with this translation, however, is that it is not clear what world "if Joe were to one-box" should refer to -- and, therefore, it is not clear how much money we should say Joe would make, "if he were to one-box". After all, Joe is a deterministic physical system; his current state (together with the state of his future self's past light-cone) fully determines what Joe's future action will be. There is no Physically Irreducible Moment of Choice, where this same Joe, with his own exact actual past, "can" go one way or the other.
To restate the situation more clearly: let us suppose that this Joe, standing here, is poised to two-box. In order to determine how much money Joe "would have made if he had one-boxed", let us say that we imagine reaching in, with a magical sort of world-surgery, and altering the world so that Joe one-boxes instead. We then watch to see how much money Joe receives, in this surgically altered world.
The question before us, then, is what sort of magical world-surgery to execute, before we watch to see how much money Joe "would have made if he had one-boxed". And the difficulty in Newcomb’s problem is that there is not one but two obvious world-surgeries to consider. First, we might surgically reach in, after Omega's departure, and alter Joe's box-taking only -- leaving Omega's prediction about Joe untouched. Under this sort of world-surgery, Joe will do better by two-boxing:
Expected value ( Joe's earnings if he two-boxes | some unchanged probability distribution on Omega's prediction ) >
Expected value ( Joe's earnings if he one-boxes | the same unchanged probability distribution on Omega's prediction ).
Second, we might surgically reach in, after Omega's departure, and simultaneously alter both Joe's box-taking and Omega's prediction concerning Joe's box-taking. (Equivalently, we might reach in before Omega's departure, and surgically alter the insides of Joe brain -- and, thereby, alter both Joe's behavior and Omega's prediction of Joe's behavior.) Under this sort of world-surgery, Joe will do better by one-boxing:
Expected value ( Joe's earnings if he one-boxes | Omega predicts Joe accurately) >
Expected value ( Joe's earnings if he two-boxes | Omega predicts Joe accurately).
The point: Newcomb's problem -- the problem of what Joe "should" do, to earn most money -- is the problem which type of world-surgery best cashes out the question "Should Joe take one box or two?". Disagreement about Newcomb's problem is disagreement about what sort of world-surgery we should consider, when we try to figure out what action Joe should take.