If the alien is able to predict your decision, it follows that your decision is a function of your state at the time the alien analyzes you. Then, there is no meaningful question of “what should you do?” Either you are in a universe in which you are disposed to choose the one box AND the alien has placed the million dollars, or you are in a universe in which you are disposed to take both boxes AND the alien has placed nothing. If the former, you will have the subjective experience of “deciding to take the one box”, which is itself a deterministic process that feels like a free choice, and you will find the million. If the latter, you will have the subjective experience of “deciding to take both boxes”, and you will find nothing in the opaque box.
In short, the framing of the problem implies that your decision-making process is deterministic (which does not preclude it being a process that you are conscious of participating in), and the figurative notion of “free will” does not include literal degrees of freedom. If you must insist on viewing it as a question of what the correct action is, it’s to take the one box. Regardless of your motivation, even if your reason for doing so is this argument, you will find yourself in a universe in which events (including thought events) have led you to take one box, and these are the same universes in which the alien places a million dollars in the box.
If the alien is able to predict your decision, it follows that your decision is a function of your state at the time the alien analyzes you. Then, there is no meaningful question of “what should you do?” Either you are in a universe in which you are disposed to choose the one box AND the alien has placed the million dollars, or you are in a universe in which you are disposed to take both boxes AND the alien has placed nothing. If the former, you will have the subjective experience of “deciding to take the one box”, which is itself a deterministic process that feels like a free choice, and you will find the million. If the latter, you will have the subjective experience of “deciding to take both boxes”, and you will find nothing in the opaque box.
In short, the framing of the problem implies that your decision-making process is deterministic (which does not preclude it being a process that you are conscious of participating in), and the figurative notion of “free will” does not include literal degrees of freedom. If you must insist on viewing it as a question of what the correct action is, it’s to take the one box. Regardless of your motivation, even if your reason for doing so is this argument, you will find yourself in a universe in which events (including thought events) have led you to take one box, and these are the same universes in which the alien places a million dollars in the box.