Actually, that premise isn't needed. No matter what the causes are, or even if I am an ontologically basic mental entity, it still remains true that I did not cause myself. I may not have been caused by anything else, but I certainly didn't determine which algorithm is making my decisions. Not to mention that the rest of the world has to affect my will somehow, or I couldn't actually perceive it or act on it intentionally (it's a simple inversion of the argument against epiphenominalism). One-way causation is easily possible; I could write a computer program that worked like that. But the very act of writing the computer program violates the "free will" in the strict knee jerk reaction sense of "determining my own actions". Determining your own actions requires cyclic causality, and even then I would struggle to accept that I really was determining my actions, rather than just saying that they happened basically by chance (I cannot recall where, but I recently saw something by EY about circular causality and time-turners in Conway's Game of Life in which he said that the only way to calculate it with a Turing machine is to iterate over all possible universes and rule out the ones where it doesn't happen by chance).