One might use computational irreducibility to says that the only way to predict your behavior is to observe your behavior. Any system that could predict you must first recreate you. For those that see determinism as undermining free will, this gives one way to conceptualize the idea that you have ownership of your choices despite determinism.
So with no power to predict the outcomes of my actions, or even predict how I will pick an action, I bear witness to myself acting anyway- and this we call free will?
What troubles me is that the more we take away any determining factors for free will the more it sounds like randomness.
You can "predict" your general disposition to respond to certain kinds of reasons given your values and so on. But you can't predict how arbitrary factors will weigh on your decision making in a given moment. E.g. you skipped breakfast and your blood sugar is low, so in this moment you happen to weigh satisfying hunger more than, say, the diet you're on. This doesn't make your decision not "up to you" just because minute factors can't all be accounted for prior to acting.
Whether there is any meaningful notion of free will here is another matter. IMO the term free will is a red-herring. We obviously make choices and those choices are attributable to us. The only relevant question is whether we have a sufficient kind of authorship over our choices such that we can/should be rendered accountable for their outcomes. But this is mostly tangential to the kinds of disputes people have about free will.
