Neurologically speaking, I'll admit that you could be right. It could turn out to be the case that humans happen to be a sort of creature that makes decisions based on neuron firings, and that neuron firings are in turn based entirely on deterministic particle collisions plus a bit of quantum randomness on the side. I keep half an eye on the neuroscience articles in the popular press, and if and when they report that conclusion, I'll take it seriously.

But this is what is so great about Bayesian epistemology. You don't have to wait for some neuroscientists to announce this finding. If you know a decent amount of neuroscience now, you can be fairly confident in predicting that they one day will be able to explain choice in terms of neuron firings. All the people here who believe this aren't just making it up. We're extrapolating from what is known and making reasonable inferences. If you wait for someone to figure out exactly how it is done you're going to spend a lot more time being wrong than those who infer in advance. Again though, I can already make accurate predictions about people's choices based on macro-phenomena.

In the meantime, I find that "choice" works just fine as a placeholder in the heuristic equations I use to model my mental macrophenomena. It may or may not correspond to anything real at the quantum level, but it helps me understand myself, so I'm using it.

But don't confuse placeholders with fundamental properties. I have no problem with "choice". I use it all the time. I think I make choices constantly. If it is helpful for your models by all means use it. But that doesn't require you to assert that choice is some incredible new kind of event which is neither causal nor random. I have lots of things in my ontology that are not in my basic ontology: morality, love, basketball etc. Maybe in modeling subjective experience you even want to distinguish things you do from other caused or random events and so use this word "choice" in a special way. But surely you can recognize that you aren't actually that different from all the other objects you discover in the world and likely work the same way they do. And when you take this objective, view from nowhere, scientific perspective I don't see how you can have an event that is neither caused nor random.

'm sorry; I'm not sure what else to say. if my analogy about red/blue/green and my necessary vs. sufficient paragraph didn't get the point across, then I don't know how else to explain it. if you insist on using a mental model that has only two possible values for a variable, then talk about a third value will not make any sense to you; I cannot stop you from trying to explain the third value in terms of your existing mental model and then getting confused or annoyed when it doesn't work.

I quite understand that your "choice" is neither caused or random but a third value that is neither. What I don't understand is what positive qualities this third value possesses. I promise you I can make sense of their being a third variable in abstract. What I don't understand is what your third variable is. I can say lots of things about "random" and "causally determined" that distinguish these properties. But I haven't heard you do anything in the way of describing this third property.

You should know that you're hardly the first person who has wanted this kind of free will and went about inventing a third kind of thing to prove that it existed. One reason I'm so skeptical is that every single one of these attempts that I know of has failed miserably. Libertarians are a very small minority among contemporary analytic philosophers for a reason.