Let's return to the idea of levels of description. An action can be described on many different levels: the electron/molecular level, the neural level, and the mental level of thoughts and desires. Very possibly there are intermediate levels of description in terms of various brain subsystems, but I don't think those levels are currently well enough understood to be very useful.
At the level of electrons, atoms, and molecules, the description ought to be quantum mechanical, and thus indeterministic.
At the level of individual neurons, the description might be effectively deterministic, or it might not. It all depends on whether the neurons act as quantum amplifiers (like the Geiger-counter-bomb) or quantum dampers (like a computer). It seems conceivable to me (having very little knowledge of neuroscience) that at times, a single ion tunneling across the cell wall could be the difference between a neuron firing or not. This would make the neuron a quantum amplifier: the randomness of the tunneling event could get amplified and end up determining whether or not you perform some action. But maybe not - maybe the neuron is more like a computer transistor, which is designed so that a few electrons more or less don't make a difference to the outcome.
What about the level of mental events? Here the description is so loose, I would find it difficult to call it deterministic. Suppose I am considering which university to attend. I have reasons in favor or against both of my top choices: one is closer, the other gave me more aid, one is small and intimate, the other is large and has lots of opportunities.... But someone else with the same list of reasons could end up with the opposite decision, without being irrational about it. I suppose we could put weights on all the reasons and devise a formula that would determine the result - but how to decide on the weights and the formula? And would it work again if I had to make the decision again? So perhaps at this level Ekstrom's "caused but not determined" makes sense.
In my opinion, many of the difficulties involved with free will are the result of confusing different levels of description. Here is Ekstrom, for example (Free Will, pp. 195-196):
The idea that we can direct our behavior by our thoughts ... is welcome, but it is only superficially comforting. It comforts until we think about the possibility that even our thoughts are driven to be what they are by previous neurophysiological events (between which there are deterministic causal links), a chain going backward through events in our childhood brains and to events prior to our birth.
Notice how she slides from the mental level, to the neural level, to the micro-physical level of "events prior to our birth" without batting an eye. (Clearly there cannot be a neural level before there are neurons, so she must be thinking here of the electronic/atomic level.)
Sometimes the argument is phrased in terms of ultimate responsibility: You cannot have ultimate responsibility for something that you do not have control over. You do not have control over the events of the distant past that are the causes of your behavior today (if determinism is true). Therefore, you do not have ultimate responsibility for your actions.
But recall the Mars rover that had to turn left or right when confronted with a large rock. It would be very strange to say the computer program that made the rover turn left doesn't have responsibility for the decision to turn left because, at the electronic level, everything is determined by the laws of physics. That seems to get the causality exactly backwards. We would rather say that the computer program, together with the computer hardware, caused the electrons to flow in such a way as to make the rover turn left. So here is one case where the higher level is the cause of what's happening at the lower level, rather than the other way around. Or perhaps this is using "cause" in a different sense - another thing I find missing in the philosophers I've read is a careful analysis of causation.
To be continued....