Some dispositions are deterministic, or nearly so. In normal conditions, in the presence of the trigger, they do their one thing. Sugar at room temperature in water dissolves. Some dispositions are indeterministic. The electron in a mixed up/down state sent through a magnetic field will go up or down; it might go up but it might also go down. We now know better than to try to define dispositions in terms of conditionals, unless perhaps we are fond of ceteris paribus or "normally" clauses, and even then defining dispositions in terms of would-conditionals is problematic. For the dispositions can be finked. Sugar is not such that it would dissolve at room temperature in water if there were a counterfactual intervener who would vaporize it as soon as it was dipped in water.
For exactly the same reason, to define a disposition as indeterministic by means of might-conditionals is problematic, and we should know better than to try. Let's say that flipping a coin has an indeterministic disposition to result in heads or in tails. But we can imagine Black, a counterfactual intervener who, as soon as the coin flies in the air, can tell which way it's going to land if it's not interfered with, and if it's not heads, he takes away the coin's disposition and makes it land heads. In the presence of Black, it's false that the coin might land tails. But the coin still has an indeterministic disposition in the presence of Black, even if it exhibits not even the least flicker of freedom (e.g., take the case where Black has access to divine middle knowledge about how the coin would go) and worries about counterfactual interveners should not talk us out of the useful notion of an indeterministic disposition.
The Principle of Alternate Possibilities (PAP) is closely analogous to a might-conditional characterization of an indeterministic disposition. And just as we now know we should not try to characterize indeterministic dispositions by means of "if ... might ..." (at least not without a dollop of "normally"), likewise we should not try to characterize freedom by means of "could have" or "might". But just as the realization that dispositions can be finked should not make us abandon the idea that some dispositions—say, quantum mechanical ones—are indeterministic, so too Frankfurt cases should not make us abandon the idea that something indeterministic is going on. It is reasonable in the face of worries about finking simply to take dispositions to be primitive, and in particular to take the notion of an indeterministic disposition with multiple outcomes (and maybe with probabilistic tendencies) to be primitive. And then it is reasonable to take it to be a necessary condition on a free choice that it is an exercises of an indeterministic disposition.
There are some pretty strong intuitions behind PAP—between Hume (inclusive) and Frankfurt (exclusive), compatibilists tended to feel the need to do justice to it, despite it being very difficult to do so satisfactorily. If a formulation of PAP can be given that is not subject to counterexamples and appears to capture a good deal of the intuitions behind PAP, there will be good reason to believe it. And I think there is such a formulation: The agent free to choose A in circumstances C has an indeterministic disposition to choose A or to choose something else in C. This seems to capture some of the intuition behind PAP, and also captures the intuition that some libertarians have that Frankfurt examples are missing something important. The down side of this formulation of PAP is that it directly denies that all dispositions are deterministic, and hence isn't going to be neutral ground. But that's fine. The neutral ground now shifts from PAP to the idea that "something like PAP is true".
Interestingly, fairly recently some compatibilists have started to try to rehabilitate PAP using dispositions (see, for instance, the references in this paper as well as this one). So the incompatibilist who makes this move will have to see if her proposed revamping of PAP is more plausible than the proposed compatibilist ones. But a revamping of PAP should be done, as PAP attempts to capture something central to our intuitions about freedom. And my point remains: to see Frankfurt examples as destroying the idea of alternatives as central to freedom is like seeing C. B. Martin's work as destroying the idea of dispositions.
