The following seems plausible to me:

D) I can't deliberate about whether or not X shall happen unless X's happening is causally connected to my deliberation in a way that gives me some degree of causal power over X's happening.

By "deliberate" here I mean "deciding whether or not to undertake actions designed to bring about X" for some X. Given that understanding of "deliberation," D) seems to fall out almost by definition. It's clear, for example, that on this understanding of "deliberation," I can't deliberate about whether or not the star Betelgeuse will go Nova tomorrow--Betelgeuse tomorrow isn't even in my light cone! Similarly, I can't deliberate about whether or not the third flight into Indianapolis will land as scheduled tomorrow. That matter simply isn't within my causal power, much less causally connected to any act of deliberation I may try to undertake concerning the matter.

But I can deliberate about whether my son will be picked up on time from school today. I'm the one who picks him up. I can decide, in this present act of deliberation, whether to undertake actions that will issue in his being picked up on time, or rather whether to undertake actions that will tend to delay my picking him up.

It seems clear--I can deliberate (in this sense of "deliberate") about what is within my power and is causally connected to my act of deliberation in a way that allows that power to be active. And if something isn't causally connected to my act of deliberation in that way, then I can't deliberate about it.

I thought.

But here's a scenario that modifies Newcomb's Problem, and which seems (to me right now) to make a problem for D).

You're on a beach, there are many stones on the ground, there is a box, and there is an alien talking to you. The alien, you know through considerable personal experience, has the power to travel through time. (Different from Newcomb's problem, which doesn't involve time travel.) And the alien is telling you that he's seen the future, and he knows that there is some number of rocks that you are going to pick up in the next few minutes and put in the box. He also knows that tomorrow, a man named Steve (you are not Steve) is going to win a lottery--and the number of stones you are going to pick up in a few minutes just happens to be identical to the number of millions Steve is going to win. This relationship between your stone up-picking and Steve's lotto winning is completely coincidental, just as it is a complete coincidence that the number of chairs at the table I'm sitting at nowin this coffee shop is identical to the number of children I have. The relationship between rocks and lotto is coincidental, yet for all that, is a real relationship. The two numbers are identical. The number of rocks you put in the box is the same as the number of millions Steve will win.

When I put myself in this scenario, I understand the following to be true. Steve's winning the lotto--and how much he wins--is not within my power to affect. Most importantly, it's certainly not within my power to affect it simply by putting rocks in a box. I can deliberate about how many rocks to put in the box, but that deliberation does not in anyway cause Steve to win however much he is going to win. The two matters are causally unrelated.

Yet, for all that, in complete violation of D) above, I can not shake the feeling that I can deliberate about how many millions Steve will win. In other words, when I am deciding how many (if any) rocks to put in the box, I can't shake the accompanying feeling that I'm also deciding how many millions Steve will win.

The problem (and this may just be a psychological problem for me rather than a philosophical problem for anyone!) is made even starker by the following modification to the scenario. Suppose Steve has already won or lost the lottery in question. I don't know Steve, and I have no access to how much he won (or whether he won at all). The alien has told me, though, that by sheer coincidence, it happens that the number of rocks I put in the box is the same as the number of millions Steve won. (Hopefully its clear that one possibility is that Steve won zero millions.)

What happened to Steve already happened. No one can have any kind of causal power over Steve's winnings. Not even the time-travel existent in this scenario obviates that fact--the alien doesn't constitute a causal connection going from present acts to past events, since all the alien is doing is reporting something about those past events to a person in the present.

And yet, even in this scenario, I can't shake the feeling that I can deliberate about how many millions Steve is to have won. (Took a bit of thought to decide what tense to use there!) It seems to m that when I am deciding what to do about the rocks, I am also deciding, via that deliberation, what shall have happened to Steve.

Steve's state is not within my control to any degree at all. Yet (it seems to me at least instinctively) I can decide how many millions Steve wins, in much the same way I can decide how many minutes shall have passed until my kid gets picked up from school.

D) seems utterly plausible to me--practically definitionally true--and yet at the same time I am convinced (not by argument, just by intuition) that I should treat a situation like the one I've just describd as a counterexample to D).

Perhaps I'm wrong in thinking I can decide anything about Steve's millions. Perhaps I should be like a two-boxer in the original Newcomb scenario and simply put (or not put) however many rocks into the box I'd like, without regard for Steve and his lotto winnings.

Or perhaps D) is simply mistaken.

Or perhaps there's something fundamentally incoherent about the scenario I described.

Or perhaps something else. What do people think?