Libertarian free will
Libertarian free will means that our choices are free from the determination or constraints of human nature and free from any predetermination by God. All "free will theists" hold that libertarian freedom is essential for moral responsibility, for if our choice is determined or caused by anything, including our own desires, they reason, it cannot properly be called a free choice. Libertarian freedom is, therefore, the freedom to act contrary to one's nature, predisposition and greatest desires. Responsibility, in this view, always means that one could have done otherwise.
Compatibilist vs. libertarian views of free will
The Compatibilist believes that free will is "compatible" with determinism (as in the sovereignty of God). The incompatibilist says that the free will is "incompatible" with determinism. The Libertarian is an incompatibilist who consequently rejects any determinism associated with the sovereignty of God. Hence, Libertarian Free Will is necessarily associated with both Open Theism, which maintains that God does not foreknow or predetermine the free choices of man, and Arminianism, which admits that God in his omniscience foresees man's free choices and reacts accordingly. Libertarian freedom is the general view of liberal Protestantism and a growing number of evangelicals.
The Compatibilist view - This view affirms that man freely chooses what God has determined that he will chose. In this way, the idea that God is in charge, and the idea that man can be held responsible for his actions are compatible ideas. Free will is affected by human nature and man cannot choose contrary to his nature and desires. This view acknowledges man as a free moral agent who freely makes choices. But due to the effects of the fall, as contained in the doctrine of total depravity, man's nature is corrupted such that he cannot choose contrary to his fallen nature -- He cannot discern spiritual things or turn to God in faith apart from divine intervention.
The Libertarian view - According to libertarianism, the idea that God causes men to act in a certain way, but that man has free will in acting that way is logically false. Free means uncaused. Man has free will, and his decisions are influenced, but not caused. God limits the actions of men, but not their mind or will. Man has the ability to turn to God in Christ and sincerely ask for help, selfishly perhaps, apart from specific (special) divine enablement. According to Arminianism, God, in his freedom, not only sets a condition on salvation and wills only to save those who would ask Him to rescue them. God, then, predestines those who He "foreknew" to salvation. Or, according to Open Theism, God is anxiously waiting to see what each person will do, for he cannot know ahead of time what the choice might be.
\1) Causality — If causes are understood as conditions prior to an effect that guarantee an effect, and all events have causes, then it follows that all events were preceded by conditions that guaranteed those events. But this is the same as saying all events are determined. Since the choices of humans are events, it follows that the choices of humans are determined.
\2) Responsibility — Rather than salvage human responsibility, some maintain that libertarian freedom destroys it. If our choices have no causes, in what sense are they our choices? Is it any more agreeable to reason to hold humans responsible for choices they didn't cause than to hold them responsible for choices that were caused and thus determined?
\3) God's Freedom — Some have maintained libertarian freedom on the basis that all things done of necessity are not worthy of praise or blame. But what are we to think of God's actions? We believe that God does good, and that God cannot do evil. Does God's moral inability to do evil make His good actions unpraiseworthy? If God must do good, is He then unpraiseworthy? Some have said that God must do good because God's nature determines His choices. God is still free, some say, because God can act in accordance with His choices, but God's choices are determined by His nature. If God's choices are determined, and God is worthy of praise, this is a clear case, some say, of actions that are determined and thus necessary while also being morally praiseworthy.