Critics of "libertarian free will" usually adopt this meaning in order to attack the idea of randomness in our decisions, which clearly would not help to make us morally responsible.

Unfortunately, even defenders of libertarian free will (Robert Kane, for example) continue to add indeterminism into the decision itself, making such free will "unintelligible" by their own account.

Despite their claim that they are better equipped than scientists to make conceptual distinctions and evaluate the cogency of arguments, professional philosophers have mistakenly conflated the concepts of "free" and "will." They (con)fuse them with the muddled term "free will," despite clear warnings from John Locke that this would lead to confusion.

Locke said very clearly, as had some ancients like Lucretius, it is not the will that is free (in the sense of undetermined), it is the mind.

John Locke liked the idea of Freedom and Liberty. He thought it was inappropriate to describe the Will itself as Free. The Will is a Determination. It is the Man who is Free. "I think the question is not proper, whether the will be free, but whether a man be free." "This way of talking, nevertheless, has prevailed, and, as I guess, produced great confusion," he said. It has and still does produce confusion

In chapter XXI, Of Power, in his Essay Concerning Human Understanding, Locke calls the question of Freedom of the Will unintelligible. But for Locke, it is only because the adjective "free" applies to the agent, not to the will, which is determined by the mind, and determines the action.

Concerning a man's liberty, there yet, therefore, is raised this further question, Whether a man be free to will? which I think is what is meant, when it is disputed whether the will be free. (s.22)

This, then, is evident, That a man is not at liberty to will, or not to will, anything in his power. (s.24)

Freedom requires some events that are not causally determined by immediately preceding events, events that are unpredictable by any agency, events involving quantum uncertainty. These random events create alternative possibilities for action.

Randomness is the "free" in free will.

In short, there must be a Randomness Requirement, unpredictable chance events that break the causal chain of determinism. Without this chance, our actions are simply the consequences of events in the remote past. This randomness must be located in a place and time that enhances free will, one that does not reduce it to pure chance.
(Determinists do not like this requirement.)

Freedom also requires an adequately determined will that chooses or selects from those alternative possibilities. There is effectively nothing uncertain about this choice.

Adequate determinism is the "will" in free will.

So there is also a Determinism Requirement - that our actions be adequately determined by our character and values. This requires that any randomness not be the direct cause of our actions. (Libertarians do not like this requirement.)

Adequate determinism means that randomness in our thoughts about alternative possibilities does not directly cause our actions.

A random thought can lead to a determined action, for which we can take full responsibility.

We must admit indeterminism
but not permit it to produce random actions
as Determinists mistakenly fear.

We must also limit determinism
but not eliminate it as Libertarians mistakenly think necessary.