It may seem intuitive to define libertarian free will (LFW) as simply having the ability to choose between (at least) two options such that nothing compels you to choose either one (or any) in particular. Analytic philosophers like using heuristic tools like the conception of logically possible worlds, and in their preferred modal vocabulary the naïve version of the libertarian thesis would look something like this:
S is Libertarian Free if and only if S is given a choice between A and B in both logically possible worlds W and W*, where W and W* both have all and only the same causal antecedents to the choice in play, and S chooses A in W but not in W*.
This definition is rife with problems, however. For instance, if the mechanism responsible for S’s choosing A or B happens to operate indeterministically (as we might imagine the quantum vacuum does – or at least, as those who subscribe to indeterministic theories of quantum mechanics think it does), and S is at the whim of this mechanism, then S satisfies the above constraint, but has not exercised what we (libertarians) mean by ‘free will.’ Thus, we need to explicitly work into the definition that the choice finds it’s origin in the free and intentional movement of the will.
In a previous article I defined Libetarian Free will as follows:
S is libertarian free =df S has at least one choice between at least two options A and B, where no causal antecedents to S’s choice determine that S chooses either A or B, and S’s choosing of A or B is an intentional act of causally determinative volition on the part of S.
This definition is also problematic in a few ways. First, S might be libertarian free dispositionally, but S has not lived long enough to encounter even a single choice between at least two options A and B. We can imagine a child who, by nature, has the undeveloped potential to make libertarian free choices, but who, for whatever reason, doesn’t live long enough to realize that potential. We can also imagine a libertarian free agent popping into existence, and then, before she ever gets the chance to exercise her freedom, popping out of existence. In such cases we have imagined libertarian free agents, but they have never been given the opportunity to exercise their freedom (and so, on my proposed definition, would not be genuine, bona fide, examples of libertarian free agents). Thus, perhaps libertarian freedom needs to be defined dispositionally:
S is libertarian free =df S has the dispositional potential to, if given at least one choice between at least two options A and B, choose A where no causal antecedents to S’s choice determine that S chooses A, and S’s choosing of A would be an intentional act of causally determinative volition on the part of S.
This definition is liable to run into problems with Frankfurt style counter-examples (depending on how one construes the word ‘choose’ in the definition). I previously dealt with this by providing a careful definition of ‘choosing,’ but the definition I put forward was at best ambiguous on its face. Without the additional caveat, it isn’t evident whether to ‘choose’ meant to act in the manner willed, or simply to signify an act of the will (i.e., primitive deciding, which is prior to action). If the first, then Frankfurt style counter-examples are going to pose a problem for libertarianism, and if the latter then they probably won’t. In the interest of disambiguation, this further amended definition should be preferred:
S is libertarian free =df S has the dispositional potential to, if given at least one choice between at least two options A and B, decide to choose A where no causal antecedents to S’s choice determine that S decides to choose A, and S’s deciding to choose A would be an intentional act of causally determinative volition on the part of S.
To my mind there are only three problems which this definition might have, but I am not (myself) convinced that these are genuine problems (in other words, I am convinced that these are at best pseudo-problems), so that I am content to subscribe to the above definition. These three problems are (i) that libertarianism is semantically vacuous (i.e., logically incoherent), (ii) that Frankfurt-style counter-examples might be made to apply even to the act of deciding to choose, and (iii) that if it makes sense to talk about an intentional act of causally determinative volition, it might make sense to imagine that a person exercises such a capacity even without being given a choice between two alternatives. The first pseudo-problem is a popular one, but there is no compelling argument for it (says me). Those who cannot see the sense in it may be intellectually colourblind (to borrow from Alexander Pruss yet again), and at least until they provide a convincing demonstration (convincing, that is, to Libertarians, and not just convincing to die-hard determinists), we are well within our rights to dismiss the claim with a measure of incredulity. The second pseudo-problem is not a real problem precisely because if one cannot even decide (in a causally un-coerced way) in favor of one option over against another (such as its negation), then we have lost sight entirely of the will as a free actor. The third pseudo-problem seems to me to be a clear pseudo-problem because even if we might perform an intentional act to realize A, if we had no genuine choice between A and ~A, then that intentional act is not causally determinative. It may be causally required (such that A could not have come about without the intentional act of the will), but it wasn’t determinative in the sense that it determined the outcome (the effect) – it would just be one more link in a causal chain running back in a line of succession before it all the way to a determinative cause.
 Alexander Pruss, The Principle of Sufficient Reason: A Reassessment. (Cambridge University Press, 2006): 193.