“Free will is a cause that is neither deterministic nor stochastic.” Although this notion is somewhat common, I would argue that this distincion (often interpreted as exclusive classification of causes) is incompatible with what we observe:
Yes, there are phenomena that are (as far as we know) fundamentally stochastic, most often associated with subatomic/“quantum” scales. And there are systems we can describe sufficiently accurate so that we view their behavior as “deterministic”, like macroscopical mechanical systems. For some, we may even prove that stochastic effects in the above sense are irrelevant (i.e. cancelled out by a system's stable behavior).
But as systems get more complex, this distinction rapidly loses its meaning:
Just observing a rather trivial system like multiple bodies driven only by their gravitational interaction over long times, yields a system where outcome depends on initial conditions at a scale below the fundamental measurability (→uncertainty relation).
Another example may be fluid dynamics, where we have to rely on a stochastic description (and often heuristic models) to describe the macroscopic behavior, while assuming underlying deterministic behavoir. But again, due to the (in a mathematical sense) unstable behavior of the system it is quite clear that ultimately, fundamentally stochastic effects contribute to the concrete pattern of flow at a certain time.
Hence, causes will be either deterministic or stochastic only for systems of very low complexity. Given the vast variety of real systems where we observe stochastic causes contributing to locally deterministic behavior, I find it highly arbitrary to choose to exclude free will, i.e. the behavior of brains, from this logic and invent something different altogether (“free will”) instead. Brains are certainly very complex systems, where deterministic effects like simple impulse conduction as well as unstable (hence potentially stochastic) effects like decision-making are omnipresent.