The trick of determinism is that it makes it sound like the initial conditions ‘choose’ the end result – they determine what happens. Yet, this is in a sense not really accurate – one may be able to predict the end result based on the initial conditions, but there are intermediaries (in this case, humans) who choose, and it is these choices that lead to the result. These choices are of course based on reasons and information – if not, what good would they be as choices? So, yes, one might be able to predict that someone will choose an apple instead of a spoonful of dirt, but that hardly undermines the autonomy of the chooser – what it means in saying we can predict this choice is that the chooser is able to take in information, and act on good reasons for doing x instead of y. This is the whole importance for being able to choose – it’s why organisms have the ability to choose. That the prediction comes true may require choosers as intermediaries.
However, I think another reason determinism seems incompatible with choice is that it seems to go along with reductionism – that ‘good reasons’ don’t really exist, but rather there are just mindless fundamental causal processes that can be used to describe a situation. So, when determinist thought experiments are set up, they sometimes involve a description of the universe in terms of fundamental, mindless causal processes. From these, so the thought experiment stipulates, one can predict some end result, that will have as intermediaries ‘choices’. Yet, this thought experiment implies, those choices in a sense don’t really matter – just the basic, mindless causal processes that go along with them do.
The most obvious response to this is: it is hypothetical, and not entailed by scenarios which involve prediction of certain sorts. It very well may not be the case that the universe works in that way, i.e., that there is no such thing as a conscious mind that can affect decision, but rather only mindless, causal processes which are then in some way reflected in the conscious mind (i.e., the mind is epiphenomenal). The idea that the universe does work this way in its entirety is somewhat speculative, and indeed, there is significant evidence that it is not true.
If one sets aside this consideration, however, and considers the thought experiment as specifying initial conditions that lead to choosers that have conscious experiences, are able to draw on memories, and then coordinate their actions based on that information and those reasons, and so on, then this implicit nihilism is no longer present, and I think the seeming incoherence between ‘determinism’ and free choice is reduced. To distinguish these kinds of cases, perhaps ‘predictionism’ would be a more useful term for the general case, which can include the causal role of conscious choosers beyond mindless, causal processes.
Of course, it might be the case that everything in the universe is determined by mindless, causal processes, and that ‘minds’ as we understand them are epiphenomena (or are abstractions of these mindless, causal processes – a kind of eliminativism). But here the ‘problem’ as far as whether ‘we’ ‘choose’ isn’t so much compatibilism (i.e., the compatibility of prediction and free choice) as a kind of reductionism.
Also see here.