The only serious argument for incompatibilism that I know is the Consequence argument due, most famously, to Peter van Inwagen. (An Essay on Free Will, OUP, 1983.)
The version I will discuss is due to David Lewis. ("Are We Free to Break the Laws?”, Theoria 47 (1981), 113-121)
He tells us to think of the argument as a reductio. A compatibilist is someone who claims that the truth of determinism is compatible with the existence of the kinds of abilities that we assume we have in typical situations in which we deliberate and make a choice. Let’s call these ‘ordinary abilities’. The Consequence argument claims that if we suppose that a deterministic agent has ordinary abilities, we are forced to credit her with incredible abilities as well.
Here is Lewis's argument.
Pretend that determinism is true, and that I did not raise my hand (at that department meeting, to vote on a proposal) but had the ordinary ability to do so. If I had exercised my ordinary ability – if I had raised my hand -- then either the remote past or the laws of physics would have been different (would have to have been different). But if that’s so, then I have at least one of two incredible abilities – the ability to change the remote past or the ability to change the laws. But to suppose that I have either of these incredible abilities is absurd. So we must reject the claim that I had the ordinary ability to raise my hand.
Van Inwagen doesn't object to Lewis's way of stating his argument. On the contrary, he has said that Lewis's paper is “the finest essay that has ever been written in defense of compatibilism – possibly the finest essay that has ever been written about any aspect of the free will problem”. ("How to Think about the Problem of Free Will”, Journal of Ethics (2008) 12, 337-341).
Van Inwagen now agrees that the Consequence argument fails as a reductio.
he claims that it has nevertheless succeeded in
"raising the price" of compatibilism. (Freedom to Break the Laws",
I disagree. I say that the argument neither succeeds as a reductio nor succeeds in "raising the price" of compatibilism - that is, the price of commonsense at a deterministic world. What the argument does achieve -- at least on Lewis's articulation of it -- is a clear statement of the counterfactuals to which the compatibilist is committed. The argument is valuable for this reason. It makes it clear that we need to understand counterfactuals in order to understand what's at stake in the free will/determinism debate. But as an argument for incompatibilism, it fails.