I recently reread Roderick Chisholm's classic paper on libertarian free will, "Human Freedom and the Self," in which Chisholm presents and defends the idea of agent causation as a solution to the standard dilemma faced by libertarians. The article seemed more insightful this time than when I first read it, but ultimately it just helped clarify to me why I think libertarian agent causation is problematic.
I did like Chisholm's defense of the very idea that the agent can be a cause, but, then again, agent causation in this restricted sense should be unobjectionable to materialists, since we identify agents with their material constituents. I am doubtful about his contention that we experience our ability to cause things to happen—I am unaware of anything beyond the constant conjunction of my will with certain bodily movements—but he seems right that as far as the direct observability of causation goes, agents enjoy at least parity with other things as wielders of causal power, since causation (as Hume pointed out) is never observable. Of course, if Chisholm means to identify the agent with some Cartesian mental substance, that's a different story, because then we become much less clear about what this thing is to which we are attributing causal power; but, in this case, the problem is with the agent's status as a thing, not, as a thing with causal power specifically. But, on a materialistic account of agency, I see nothing (well, nothing special) to worry about.
The real sticking point is in the idea of the agent as prime mover, and this is something that applies, more generally, to any libertarian conception of a free prime mover. The problem is that we don't just want agents to be causes; they must be free causes. And what do we mean by this? Certainly, that their actions must not be necessitated by their desires. But, there is more to it than this. We also require that the agents control the decision of how to act. And that is something I don't think Chisholm or anyone else has been able to provide a coherent picture to, at least so far.
Let me try to flesh out my worry by providing a picture that gets us as close to libertarian agency as I think we can get. Libertarians are quite right that there is no dichotomy between determinism and strict randomness, where the latter is understood as saying that my actions will be haphazard. We can weight actions with probabilities, so that the agents' decisions will be influenced without necessitation. My analogy for this is the standard interpretation of quantum mechanics. Suppose we are interested in some observable O, of which a system can have one of two possible values, O1 or O2. We can (in general), prepare a system in such a state that it has, say, a 3/4 probability of taking on value O1 upon measurement, and a 1/4 probability of taking on value O2. Which of these happens is purely a matter of the probabilities. So, in this situation, we have an event that is not determined, but heavily influenced, by the previous total physical state of the universe. Why not understand free actions in this way, with the sum of our desires standing in for the state of the system, and our free decisions standing in for the measurements?
The thing that is missing from this picture, that makes it incompatible with free will, is that nothing in the quantum mechanical picture (the system, the measuring device, or anything at all) dictates which of the outcomes will in fact occur. Nothing controls the outcome of the collapse. The prior state of the system controls the probabilities, but there is absolutely nothing that chooses the actual outcome. If we imagined there were something (let's call it an "agent") that chose the outcome, then the only way we could get the agent's actions to match the probabilities would be by making its choice random, like having it shut its eyes, throw a dart at a board that is 3/4 red and 1/4 black, and having it act on that basis. But in this case, the agent still doesn't have the right kind of control over the outcome, because there is a random process at the basis of its decision. The agent may just as well be a robot that is hooked up to a random number generator and a program that assigns weights to different arm movements: the robot acts, and is needed for the act, but it isn't really choosing anything at all.
There are more sophisticated accounts of libertarian free will than Chisholm's, but none of them appear to me to solve this problem. Attempts to bypass it all seem to end up either in obscurity or in a semantically-cloaked retreat to compatibilism. If my assessment is accurate, and extends to the accounts I have not yet studied, then that is only to be expected, because the classic dilemma gets it right: neither determinism nor indeterminism is compatible with libertarian free will—there is no logical space for the position at all.
Not that I am sure enough about that to stop studying new attempts, or new defenses of old ones.