In considering this article, remember that Compatibilism is the perspective of Calvinism regarding moral freedom and libertarianism is the perspective of Extensivism (non-Calvinism). Many compatibilists argue that what is known as the Frankfurt counterexamples demonstrate the falsehood of the principle of alternative possibilities (PAP) associated with libertarian freedom—that a person, in at least some scenarios, could have chosen differently. Thus, if successful, the Frankfurt counterexamples would minimize the objections libertarians have to compatibilism by demonstrating how true free, otherwise, choice can exist within compatibilism’s determinism.
In 1966, Harry G. Frankfurt developed examples that purportedly, according to some compatibilists, falsified PAP by showing how a person can make a free choice without the ability to have chosen otherwise. If true, it would bolster the claim of compatibilists and Calvinism, which is that determinism and moral responsibility, free choice, are compatible, something libertarianism rejects.
For example, Frankfurt proposed a controller who could stop or cause any action but only did so if the person was choosing the action the controller did not want him to choose. If the individual chose what the controller wanted him to choose (A), the individual made a free choice without alternative possibilities since if he did choose B (what the controller did not want him to choose), the controller would override him. Succinctly, if the controller wanted Bill to choose A and Bill chose A, he did so freely since the controller did not interfere. But if Bill chose B, the controller would override him; thus, we are supposed to conclude that Bill’s choice of A was free even though he did not have PAP— could not have chosen B because the comptroller would have overridden him.
Here is my brief response. First, it seems that for any Christian, this view of God (who would be the controller from a Christian perspective) is so contrary to Scripture as to be without merit or maybe even blasphemous. Second, while such a state of affairs might be possible once or even a few times, it does seem improbable long term, especially if you multiply it by billions of lives. Further, it does create at least a half puppet of every person, but no one but the controller knows which half. Moreover, the libertarian would say that every override by the controller results in the person not being responsible for that event.
Third, and most importantly, it did not seem to falsify PAP since all that is necessary for the PAP is that the individual can act or refrain (choose A, B, or neither). That is to say, even though the controller would have overridden Bill’s choice of B, Bill’s choice of B still entailed his choices not to refrain from acting at all and to not to choose A. Or we could say that Bill made a free choice to refrain from choosing A, which resulted in the controller’s intervention at a later point when Bill chose B; hence, he had otherwise choice not to act at all or in not choosing A before he chose B.
Because of these three things and more (if further considered), libertarians say the Frankfurt counterexamples failed to falsify PAP. Frankfurt failed to diminish the micro-deterministic nature of compatibilism, which I think biblically, logically, and practically (as we live our ordinary daily lives) is an inadequate view of the moral freedom of people. I have yet to know of a person who speaks, writes, chooses, or lives in any meaningful sense as a determinist. Linda Zagzebski says, “If when you do an act you cannot do otherwise, you do not do the act freely.” Even if it were the case, that alternative possibilities did not exist, Robert Kane says, “Fortunately, there is another place to look for reasons that free will might conflict with determinism . . . even more important than AP [alternative possibilities] . . . I call it Ultimate Responsibility, or UR.” He does note that to “dispense with AP altogether . . . would be a mistake.” 
Consequently, even with attempts like Frankfurt counterexamples, compatibilism leaves Calvinism with a micro-deterministic perspective of moral responsibility wherein a person’s greatest desires are the result of determinative antecedents, and, therefore, a person can be the proximate cause of his actions or forming his character, but he can never be the ultimate cause as is true in libertarian freedom; therefore, in compatibilism, as applied to Christianity, God stands at the origin or head of the causal chain of determinative antecedents and is, therefore, the ultimate cause of every thought and action, righteous and evil.
To mitigate or even obfuscate God’s ultimate responsibility for people choosing evil or to disobey God, Calvinists often point to the fact that God uses secondary causes. But this is merely a distraction rather than a solution in a compatibilist system of moral freedom. The number of intermediary causes involved between the proximate cause (the actor) and the ultimate cause (God) does nothing to relieve God of desiring each act (evil or good). And this to the degree that he ultimately caused the determinative antecedents which resulted in the greatest desire of the actor from which he freely chose even though at the moment of the decision, he could not have chosen differently. This conclusion stands true even if God uses secondary, tertiary, quaternary, quinary, senary, septenary, octonary, nonary, and denary causes between evil and God.
 COMPATIBILISM: Determinism and moral responsibility are compatible, hence the name. This compatibility is not achieved by compatibilism being less deterministic than hard determinism. Rather, it is achieved by defining free choice to mean as long as a person chooses according to his greatest desire, he has made a free choice for which he is morally responsible; even though given the same past, he cannot choose differently in the moral moment of decision.
Consequently, the difference between compatibilism (soft determinism) and hard determinism is not to be found in the levels of the deterministic nature of each since they are the same. Rather, the difference is compatibilism simply contends people are morally responsible for their choices if they are made according to their greatest desire, and hard determinism says they are not. Therefore, moral responsibility is the product of defining free choice as a person acting in accordance with his greatest desire even though the greatest desire is determined.
LIBERTARIAN: Man is not determined. He has the actual ability to choose between accessible options, at least in some scenarios. Libertarians contend determinism is not compatible with moral responsibility. Man possesses actual otherwise choice and can, therefore, act or refrain in the moral moment of decision, given the same past within a given range of options.
Extensivism (my term for non-Calvinism) argues God endowed man with this ability, which is an aspect of being created in the image of God. God determines the range of options. Adam’s range of options, the result of creative grace, was greater than mankind’s options after the fall. Fallen man can still choose between options, but the range of options is less than man had prior to the fall. This lessening includes losing the ability to make choices that are inherently righteous or spiritually restorative (making one right with God) based solely on creative grace. In order to make an inherently righteous choice or one that is spiritually restorative, God had to provision redemptive grace—enablements—which he did.
 They also speak inconsistently with compatibilism when interpreting Scripture, life, following God, prayer, preaching, teaching, counseling, and discussing ideas. To see this, one only needs to listen to them or read their sermons and writings.
 Linda Zagzebski, “Recent Work on Divine Foreknowledge and Free Will” in Robert Kane (ed.), The Oxford Handbook of Free Will, (Oxford: Oxford University Press, 2002), 57 DOI:10.1093/oxfordhb/9780195178548.003.00050. see also https://philpapers.org/rec/ZAGRWO.
 Linda Trinkaus Zagzebski, The Dilemma of Freedom and Foreknowledge (New York: Oxford University Press 1991), 50.
 Kane goes on to say, “The idea is this: to be ultimately responsible for an action, an agent must be responsible for anything that is a sufficient reason (condition, cause, or motive) for the occurrence of the action. If for example, a choice issues from, and can be sufficiently explained by, an agent’s character and motives (together with background conditions), then to be ultimately responsible for the choice, the agent must be at least in part responsible, by virtue of choices or actions voluntarily performed in the past, for having the character and motives he or she now has.” Robert Kane, “Some Neglected Pathways in the Free Will Labyrinth,” The Oxford Handbook of Free Will (New York: Oxford University Press, 2002), 407.
 Robert Kane, “Some Neglected Pathways in the Free Will Labyrinth,” The Oxford Handbook of Free Will (New York: Oxford University Press, 2002), 409.