You might have to answer ata's question before I can say more. But try this. Take a stock example of a free choice. Smith finds a wallet on the ground. He decides to return it. Why did he return it? Now maybe Smith didn't choose to return it, maybe someone made him do it by hypnotizing him. This is obviously a causal event, presumably we can agree that Smith isn't using libertarian free will here. But maybe he did choose to return it. Even then though we don't just stop wonder "why?". When we ask for an explanation of behavior "I chose to" isn't enough. Usually we ask for reasons. Reasons are significant explanations for actions because they appear to be morally significant. We don't usually hold drugged or (were it to happen) mind-controlled people responsible for their actions to the same degree people he choose to act based on reasons. But reasons are still causal explanations. Were returning the wallet not the moral thing to do (say the wallet had proof the owner had committed a heinous crime) then the Smith would have no returned the wallet. Explanations based on reasons can be reduced to sentences about neurons and biochemistry the same way any causal explanation can. The only explanation that I can think of that wouldn't be a causal explanation is if the choice to return the wallet just happened. There was no reason, no cause. It just happened. It could have not happened but in did. Thats what we mean by undetermined or random. There is a middle ground, some things can be more likely than other things. Some philosophers have tried to argue that brains are sensitive enough to quantum level indeterminacy that our actions cannot be perfectly predicted even in principle. But even if this is why Smith returned the wallet it obviously doesn't give Smith the kind of free will libertarians want.

I just don't know what this other thing could be. Determined and indeterminate appear to exhaust the possibility space. Philosophers have tried for a very long time to offer something else up but they inevitably fail.