It seems like this might become a discussion of Aleatory vs Epistemic Uncertainty. I like this way of describing the distinction between the two (from here—pdf):

In distinguishing between aleatory variability and epistemic uncertainty it can be helpful to think how you would describe, in words, the parameter under consideration. If the parameter sometimes has one value and sometimes has another values, then it has aleatory variability. That is, the variability is random. If the parameter always has either one value or another, but we are not sure which it is, then the parameter has epistemic uncertainty.

I believe that the differences between classical decision theory and FDT’s only occur in the context of aleatory uncertainty (although in some formulations of newcomb’s paradox there’s no actual uncertainty). That is, if you are in an epistemically uncertain environment, then FDT and classical decision theory will agree on all problems (hopefully by saying this I can cause someone to come up with a juicy counterexample).

In your example, it is unclear to me what sort of uncertainty the problem possesses because I don’t know enough about the oracle.

In the simple example where a quantum coin with a 99% chance of coming up heads is flipped to determine whether the oracle gives the right answer or the wrong answer, then the answer I gave above is right. Use expected value under the assumptions of FDT; classical decision theory will lead you to 2-box and that would lower your expected gains.

In your example relying on demographic information, it will depend a bit on what sorts of information count as “demographic” in nature. If you are, in this moment by reading this comment on lesswrong, forming the sort of self that will result in you 1-boxing or 2-boxing and that information is also an input to this sort of oracle, then I encourage you to 1-box on the oracle you had in mind.

Would a play format work? e.g.

“Iarwain (languidly): I don’t know that I am much interested in your family life, Lintamande”

Someone would have to translate the various profile pictures into emotions, but I would expect there to only be a handful of them per character.