Below be attempts at defining that what goes by the name:
libertarian free-will.
Ye be warned.
Simply put, libertarian freedom is at least the ability to choose between or among a range of alternative options each of which is compatible with one's nature at a given moment.
Timothy Stratton; Human Freedom, Divine Knowledge, and Mere Molinism. p. 24
Free-will: that which entails the capacity to originate causal chains while precluding one from having their every impulse pre-determined by antecedent conditions.
Me, here.
“Libertarianism is the view that human beings are [libertarianly]-free, where a person is [libertarianly]-free if and only if she makes at least some decisions that are such that (a) they are both undetermined and appropriately nonrandom, and (b) the indeterminacy is relevant to the appropriate nonrandomness in the sense that it generates the nonrandomness, or procures it, or enhances it, or increases it, or something along these lines.”
Mark Balaguer. Free Will As An Open Scientific Problem (pg. 7)
“…what is critical to free will is not the ability to choose differently in identical circumstances but rather not being caused to do something by causes other than oneself.”
William Lane Craig, http://www.reasonablefaith.org/free-will
That by which an agent is, once or more, the causal origin of its action.
Me, here.
The categorical ability of the will to refrain or not refrain from a given moral action. Self-determined, not determined by factors beyond the accountable agent's control. Contra-Causal, the moral ability to choose otherwise.
Here