Alternative possibilities for action are one of two criteria considered essential for libertarian free will and for moral responsibility. The other is to the ability to choose and do otherwise in exactly the same circumstances.
The Principle of Alternate Possibilities
In 1969 Harry Frankfurt defined what he called "The Principle of Alternate Possibilities" or PAP.
a person is morally responsible for what he has done only if he could have done otherwise.
Frankfurt's thought experiments are attacks on the PAP principle. His basic claim is as follows:
The principle of alternate possibilities is false. A person may well be morally responsible for what he has done even though he could not have done otherwise. The principle's plausibility is an illusion, which can be made to vanish by bringing the relevant moral phenomena into sharper focus.
Frankfurt posits a counterfactual demon who can intervene in an agent's decisions if the agent is about to do something different from what the demon wants the agent to do. Frankfurt's demon will block any alternative possibilities, but leave the agent to "freely choose" to do the one possibility desired by the demon. Frankfurt claims the existence of the hypothetical control mechanisms blocking alternative possibilities are irrelevant to the agent's free choice. This is true when the agent's choice agrees with the demon, but obviously false should the agent disagree. In that case, the demon would have to block the agent's will and the agent would surely notice.
Frankfurt changed the debate on free will and moral responsibility with his hypothetical intervening demon. Recent philosophical literature contains many articles with "Frankfurt-type cases," examples of Frankfurt's attempt to defend moral responsibility in the absence of alternative possibilities. For example, John Martin Fischer's Semi-compatibilism assumes with Frankfurt that we can have moral responsibility, even if determinism (and/or indeterminism) is incompatible with free will.
John Martin Fischer is best known for the view of "semi-compatibilism" - the idea that moral responsibility is compatible with determinism, whether free will is or is not compatible with determinism. He says that alternative possibilities for action are not required for moral responsibility in his semi-compatibilism.
we have sought to defend the idea that the sort of control that involves alternative possibilities is not required for moral responsibility. Thus, we have attempted to remove what is probably the most significant objection to the compatibility of causal determinism
Peter van Inwagen
Peter van Inwagen assumes that if there were alternative possibilities for action they would all have equal probabilities. He further assumes, in his "Mind argument" (a version of the standard argument against free will), that the random possibilities are the direct cause of action. He shows this by imagining instant replays of the universe in exactly the same circumstances.
Now let us suppose that God a thousand times caused the universe to revert to exactly the state it was in at t1 (and let us suppose that we are somehow suitably placed, metaphysically speaking, to observe the whole sequence of "replays"). What would have happened? What should we expect to observe? Well, again, we can't say what would have happened, but we can say what would probably have happened: sometimes Alice would have lied and sometimes she would have told the truth. As the number of "replays" increases, we observers shall — almost certainly — observe the ratio of the outcome "truth" to the outcome "lie" settling down to, converging on, some value. We may, for example, observe that, after a fairly large number of replays, Alice lies in thirty percent of the replays and tells the truth in seventy percent of them — and that the figures 'thirty percent' and 'seventy percent' become more and more accurate as the number of replays increases. But let us imagine the simplest case: we observe that Alice tells the truth in about half the replays and lies in about half the replays. If, after one hundred replays, Alice has told the truth fifty-three times and has lied forty-eight times, we'd begin strongly to suspect that the figures after a thousand replays would look something like this: Alice has told the truth four hundred and ninety-three times and has lied five hundred and eight times. Let us suppose that these are indeed the figures after a thousand  replays. Is it not true that as we watch the number of replays increase we shall become convinced that what will happen in the next replay is a matter of chance.
- David Widerker and Michael McKenna, Moral Responsibility and Alternative Possibilities, Ashgate, 2006
- Harry Frankfurt, "Alternate Possibilities and Moral Responsibility", Journal of Philosophy, 66/23 (1969), 829-39
- Harry Frankfurt, "Alternate Possibilities and Moral Responsibility" Journal of Philosophy, 66/23 (1969), 829-39
- Robert Kane, A Contemporary Introduction to Free Will, 2005, p.87
- David Widerker, "Blameworthiness and Frankfurt's Argument Against the Principle of Alternative Possibilities", Moral Responsibility and Alternative Possibilities, ed. David Widerker and Michael McKenna, 2006, p.53-54
- Carl Ginet, "In Defense of the Principle of Alternative Possibilities: Why I Don't Find Frankfurt's Argument Convincing," in Tomberlin ed., Philosophical Perspectives 10: Metaphysics (1996)
- John Martin Fischer and Mark Ravizza, Responsibility and Control: A Theory of Moral Responsibility, p.227
- Peter van Inwagen, "Free Will Remains a Mystery," Philosophical Perspectives, vol. 14, 2000, p.14