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AnnaSalamon comments on Confusion about Newcomb is confusion about counterfactuals - Less Wrong
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This is the issue. I suspect that Newcomb-like problems aren't meaningfully possible. Once you "explain" the problem to a machine, its choice actually causes the box to be full or empty. Omega's prediction functions as causation-without-being-causal, which makes some sense to our minds, but does not seem like it would be understood by a machine. In other words, the reason CDT does not work for a machine is because you have the inputs wrong, not the algorithm. A machine that interpreted information correctly would understand its actions as causal even if it didn't know how they did so, because it's a key assumption of the problem that they are functionally causal. If the program does not have that key assumption available to it, it should rationally two box, so it's totally unsurprising that prohibiting it from "understanding" the causal power of its decision results in it making the wrong decision.
Your counterexample is also problematic because I understand your prediction mechanism; I know how you will analyze my program, though there's some small chance you'll read the code wrong and come to the wrong conclusion, much like there's some chance Omega gets it wrong. Thus, there's a directly apparent causal connection between the program's decision to one-box and you putting the money in that box. CDT thus appears to work, since "program one-boxes" directly causes one-boxing to be the correct strategy. In order to make CDT not work, you'd need to arbitrarily prevent the program from incorporating this fact. And, if I were really, really smart (and if I cared enough), I'd design a program that you would predict would one-box, but actually two-boxed when you put it to the test. That is the winningest strategy possible (if it is actually possible); the only reason we never consider it with Omega is because it's assumed it wouldn't work.
At this moment, I agree with Psychohistorian that the apparent conundrum is a result of forcing a distinction about causality when there really isn't one.
On the one hand, we say that the contents of the boxes are not directly, causally related to our choice to one box or two box. (We assert this, I suppose, because of the separation in time between the events, where the boxes are filled before we make our choice.)
On the other hand, we say that Omega can predict with great accuracy what we choose. This implies two things: our decision algorithm for making the choice is pre-written and deterministic, and Omega has access to our decision making algorithm.
Omega bases the contents of the box on the output of our decision making algorithm (that he simulates at time (t-y)) so the contents of the box are directly, causally related to the output of our decision algorithm.
Seems wrong to say that the contents of the box are not causally related to the output of our decision algorithm at time t (i.e., our choice), but are causally related to the output of the decision algorithm at time (t-y) -- even though the decision algorithm is deterministic and hasn't changed.
In a deterministic system in which information isn't lost as time progresses, then the time separation between events (positive or negative) makes no difference to the causality ... "a causes b" if b depends on a (even if b happens before a). For example, afternoon rain will cause me to bring my umbrella in the morning, in an information-complete system.
Later edit: This represents the location in {comment space}-time where (I think) I've understood the solution to Newcomb's problem, in the context of the substantial clues found here on LW. I had another comment in this thread explaining my solution that I've deleted. I don't want to distract from Anna's sequence (and I predict the usual philosophical differences) but I've kept my deleted comment in case there are more substantial differences.
I would say that the ambiguity/double think about causality is actually the feature of Newcomb's problem that helps us reduce what causality is.
I'd say go ahead and distract. I'd love to see your solution.
How about if I send you my solution as a message? You can let me know if I'm on the right track or not...