In the many debates we've had with Arminians here, every singly one of them has brought up PAP (principle of alternative possibilities) as necessary for moral responsibility, and an obvious intuition that only one committed to determinism could deny.
However, many indeterminists deny PAP. Increasingly more and more, in fact.
Here's a few representative samples:
William Lane Craig: "But as you note, I’m a libertarian who thinks that causal determinism is incompatible with freedom. That doesn’t imply that I hold to the Principle of Alternative Possibilities (PAP), which states that a free agent has in a set of circumstances the ability to choose A or not-A. I’m persuaded that so long as an agent’s choice is not causally determined, it doesn’t matter if he can actually make a choice contrary to how he does choose. Suppose that God has decided to create you in a set of circumstances because He knew that in those circumstances you would make an undetermined choice to do A. Suppose further that had God instead known that if you were in those circumstances you would have made an undetermined choice to do not-A, then God would not have created you in those circumstances (maybe it would have loused up His providential plan!). In that case you do not have the ability in those circumstances to make the choice of not-A, but nevertheless your choice of A is, I think, clearly free, for it is causally unconstrained—it you who determines that A will be done. So the ability to do otherwise is not a necessary condition of free choice."
Michael Bergmann: "One thing that makes Frankfurt’s proposed counterexample to PAP interesting is that it is supposed to be successful even if the sort of moral responsibility at issue is fairly robust – i.e., of the sort in which an incompatibilist and not merely a compatibilist is interested. Recently, however, Frankfurt’s criticism of PAP has come under attack precisely because it (supposedly) fails when the focus is full-blooded moral responsibility of the sort that incompatibilists care about.[ii] The suggestion is that such counterexamples to PAP are successful only if one assumes the falsity of incompatibilism.
In this paper, I will defend Frankfurt’s criticism against this charge. My aim is to design a Frankfurt-style counterexample to PAP that doesn’t take for granted the falsity of incompatibilism."
David Hunt: "For example, if I murder someone, and in so doing satisfy the most exacting conditions for free will, except that an irresistible power (a demon, crazed neurologist, etc.) would have forced me to murder the person if I hadn’t done so on my own, this last factor does not appear to mitigate my responsibility in the least. Here no alternative to murder is available to me (so PAP is unsatisﬁed), but I am nevertheless free and responsible for what I do, since the factor excluding alternatives makes no causal contribution to my actions, and indeed makes no difference to what actually happens. The same can be said in cases involving divine foreknowledge. God’s foreknowledge of the murder may make it unavoidable, but it does so without making any causal contribution to murder, which would have occurred just as it did in the absence of divine foreknowledge."
--David Hunt, ‘On Augustine’s Way Out’, Faith and Philosophy, Volume 16, Number 1, (January 1999), 17.
Linda Zagzebski: some philosophers have argued that PAP is false even if we have libertarian free will. I have given such an argument (Zagzebski 1991), as has David Hunt (1999). Hunt (1996b, 1999) argues that the rejection of PAP from the perspective of a defender of libertarian freedom can be found in Augustine, but even if that is true, it is not a position historically associated with Augustine. The literature that clearly distinguishes the claim that free will requires alternate possibilities from the claim that free will requires the falsehood of determinism is contemporary. The former is a thesis about events in counterfactual circumstances, whereas the latter is a thesis about the locus of causal control in the actual circumstances. Aside from the foreknowledge literature, support for the rejection of PAP from the perspective of a free will/determinism incompatibilist can be found in Stump (1990, 1996), Zagzebski (2000), and Pereboom (2000).
Eleonore Stump: "Some defenders of the principle of alternative possibilities (PAP) have responded to the challenge of Frankfurt-style counterexamples (FSCs) to PAP by arguing that there remains a flicker of freedom -- that is, an alternative possibility for action -- left to the agent in FSCs. I argue that the flicker of freedom strategy is unsuccessful. The strategy requires the supposition that doing an act-on-one''s-own is itself an action of sorts. I argue that either this supposition is confused and leads to counter-intuitive results; or, if the supposition is acceptable, then it is possible to use it to construct a FSC in which there is no flicker of freedom at all. Either way, the flicker of freedom strategy is ineffective against FSCs. Since the flicker of freedom strategy is arguably the best defense of PAP, I conclude that FSCs are successful in showing that PAP is false. An agent can act with moral responsibility without having alternative possibilities available to her."
--Eleonore Stump, 'Alternative possibilities and moral responsibility: The flicker of freedom.' (1999) Journal of Ethics 3 (4):299-324.