David Hume's compatibilism starts from a deliberately deflationary definition: liberty, he argued, is nothing more than a power of acting or not acting according to the determination of the will, and the only alternative to this kind of liberty is not some grander metaphysical freedom from causation but constraint, being physically prevented from doing what one wills, as in imprisonment; on this view, asking whether the will itself was caused is simply a different question from asking whether a person is free, and Hume thought the two had been wrongly conflated by disputants on both sides of the free will debate for no good reason.
Harry Frankfurt sharpened the picture considerably in the twentieth century, arguing that what makes a choice genuinely free is not merely acting on one's strongest desire, which even an addict does, but acting on a desire the person reflectively endorses at a higher level, a second-order desire about which first-order desire should move them; an addict who wishes he did not want the drug is, on Frankfurt's analysis, unfree in a specific sense even while satisfying his own immediate desire, precisely because that desire is not one he endorses on reflection. This distinction lets compatibilists explain why some caused actions feel free and others do not without ever having to deny that both were, in the end, fully caused.