Suppose libertarian free will exists. Say that a person is presented with choices A and B, and she chooses A. Then, her memory is wiped, and her brain, body, and surrounding conditions are reset to the exact same conditions as when she chose A the first time. The only difference is that she is at a different point in the timeline and that she, though unknowingly, has chosen A before. Will she necessarily choose A again? Will she possibly choose B?
I want to know what philosophers believe about the implications of libertarian free will in a situation like this. To me, there are problems with both views. If she necessarily chooses A, then free will would seem independent of time and fundamental to the person. The problem is that it doesn't seem as if she made a free choice the second time, since it had to be the same as the first time. On the other hand, if she could possibly choose B, then free will seems to merely be dependent on the point in time, and it is hard to assign praise, blame, reward, or punishment to her for choosing A, if the same person might have chosen B in the same situation.
To me, the former (always choosing A) is more palatable than the latter (maybe choosing B), but both are puzzling. I can perhaps explain the former situation by saying that she makes the choice once and for all outside of time in a spiritual realm, whereas the latter situation is simply disturbing and chaotic.
Is there an option philosophers believe is more harmonious with the concept of libertarian free will? Are they divided on this? Has this been discussed much at all?