Alternative Possibilities are one of the key requirements for the freedom component of free will, critically needed for libertarian free will.

Alternative Possibilities have been part of the problem of free will at least from the time of Thomas Hobbes, who denied anyone ever "could have done otherwise".

In 1961, Harry Frankfurt famously 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 developed sophisticated arguments (thought experiments) to disprove this principle using what is known as a Frankfurt controller, but might be called Frankfurt's Demon.

The Frankfurt is a hypothetical agent who can control the minds of others, either a "nefarious neuroscientist or a demon inside one's mind that can intervene in our decisions. Considering the absurd nature of his counterfactual intervener, the recent philosophical literature is surprisingly full of articles with "Frankfurt-style cases" supporting Frankfurt, and logical counterexamples to his attack on the principle of alternate possibilities. This work is based on a logical fallacy

Frankfurt's 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."

Libertarians like Robert Kane, David Widerker, and Carl Ginet have mounted attacks on Frankfurt-type examples, in defense of free will.

The basic idea is that in an indeterministic world Frankfurt's demon cannot know in advance what an agent will do. As Widerker put it, there is no "prior sign" of the agent's de-liberate choice. This is the epistemic Kane-Widerker Objection to Frankfurt-style cases.

In information theoretic and ontological terms, the information about the choice does not yet exist in the universe. So in order to block an agent's decision, the intervening demon would have to act in advance.

That would eliminate the agent's control and destroy the presumed "responsibility" of the agent for the choice, despite no available alternative possibilities. This is the ontological Information Objection.

According to Daniel Dennett's Default Responsibility Principle, the Frankfurt controller is now responsible, not the agent.

Here is a discussion of the problem, from Kane's A Contemporary Introduction to Free Will, 2005, (p.87)

5. The Indeterminist World Objection

While the "flicker of freedom" strategy will not suffice to refute Frankfurt, it does lead to a third objection that is more powerful. This third objection is one that has been developed by several philosophers, including myself, David Widerker, Carl Ginet, and Keith Wyma.⁵ We might call it the Indeterministic World Objection. I discuss this objection in my book Free Will and Values. Following is a summary of this discussion:

Suppose Jones's choice is undetermined up to the moment when it occurs, as many incompatibilists and libertarians require of a free choice. Then a Frankfurt controller, such as Black, would face a problem in attempting to control Jones's choice. For if it is undetermined up to the moment when he chooses whether Jones will choose A or B, then the controller Black cannot know before Jones actually chooses what Jones is going to do. Black may wait until Jones actually chooses in order to see what Jones is going to do. But then it will be too late for Black to intervene. Jones will be responsible for the choice in that case, since Black stayed out of it. But Jones will also have had alternative possibilities, since Jones's choice of A or B was undetermined and therefore it could have gone either way. Suppose, by contrast, Black wants to ensure that Jones will make the choice Black wants (choice A). Then Black cannot stay out of it until Jones chooses. He must instead act in advance to bring it about that Jones chooses A. In that case, Jones will indeed have no alternative possibilities, but neither will Jones be responsible for the outcome. Black will be responsible since Black will have intervened in order to bring it about that Jones would choose as Black wanted.

In other words, if free choices are undetermined, as incompatibilists require, a Frankfurt controller like Black cannot control them without actually intervening and making the agent choose as the controller wants. If the controller stays out of it, the agent will be responsible but will also have had alternative possibilities because the choice was undetermined. If the controller does intervene, by contrast, the agent will not have alternative possibilities but will also not be responsible (the controller will be). So responsibility and alternative possibilities go together after all, and PAP would remain true—moral responsibility requires alternative possibilities—when free choices are not determined.⁶

If this objection is correct, it would show that Frankfurt-type examples will not work in an indeterministic world in which some choices or actions are undetermined. In such a world, as David Widerker has put it, there will not always be a reliable prior sign telling the controller in advance what agents are going to do.⁷ Only in a world in which all of our free actions arc determined can the controller always be certain in advance how the agent is going to act. This means that, if you are a compatibilist, who believes free will could exist in a determined world, you might be convinced by Frankfurt-type examples that moral responsibility does not require alternative possibilities. But if you are an incompatibilist or libertarian, who believes that some of our morally responsible acts must be undetermined you need not be convinced by Frankfurt-type examples that moral responsibility does not require alternative possibilities.

5. See Robert Kane, Free Will and Values (Albany, NY: SUNY Press 1985) p. 51; David Widerker "Libertarianism and Frankfurt's Attack or the Principle of Alternative Possibilities," Philosophical Review, 104 1995: 247-61; Carl Ginet "In Defense of the Principle of Alternative Possibilities: Why I Don't Find Frankfurt's Argument Convincing,' Philosophical Perspectives 10, 1996: 403-17; Keith Wyma, "Moral Responsibility and the Leeway for Action," American Philosophical Quarterly 34 (1997): 57-70.
6. Kane, 1985, p. 51.
7. Widerker, 1995, 248ff.