The compatibilist wants to show that we can still be free and responsible for our own actions and they can be determined. David Hume, a skeptic philosopher, tried to show this is the case on a naturalistic framework. Theist determinists adopt some of Hume's arguments and augment them in order to argue that it is possible that all our actions have been pre-determined, but we freely do those actions and are therefore responsible for them. There have also been other attempts at trying to show that this is possible.
The incompatibilist thinks this is counterintuitive. It seems to be a logical contradiction to say we are determined yet free. The libertarian argues that it is obvious that God is not the author of sin because human beings have libertarian free will, in which case they can choose between available options and none of those options is unable to be chosen. No former states of the universe or outside agents necessitate what we choose. We may be influenced by different things, but those influences do not determine what we do. The libertarian argues that this is the only way to be able hold individuals responsible for what they do. Only if it is possible to choose a counterfactual possibility is the agent responsible for what they actually choose. This is called the principle of alternate possibilities.
The libertarian argues that God is not the author of evil because He is not the one performing the evil acts that are committed. It is the creatures He created who freely chose to sin against God. They had the choice to obey or to sin and they chose to sin. If this sin originates from the creature, then the creator is not responsible for that sin.
Some determinists have tried to construct a dilemma in which the libertarian becomes trapped by their own logic. James Swan of Alpha and Omega Ministries constructs it as follows (full post found here):
When non-Reformed people argue against the Reformed understanding of sovereignty, I have to immediately ask them how they also avoid their own argument. If we apply their argument against their own position what happens? They similarly believe God created all that is, and knew the beginning from the end before He created. If I knew in advance that a person was going to get in their car by their own choice, and while driving down the road strike and kill someone, and I let them do it, I share responsibility. It's actually a severely culpable responsibility because I knew and they didn't. When God chooses to create knowing full well what evil will happen, and creates anyway, I don't see how a non-Reformed person can avoid the same charge they place on us (emphasis his).
At first glance this looks hard to get out of, at least it did to me, but the answer to this is surprisingly simple. Mr. Swan tries to show that the foreknowledge of what will happen in allowing this person (let's call him Steve) to take the car makes us responsible for what he does with the car. This seems to be a problem for Mr. Swan. He needs to show that there is a logical reason to impute the responsibility of the actual car accident to the person allowing Steve to take his car. The simple fact that the car owner knew that Steve would cause this accident doesn't seem to be a reason to impute responsibility of that particular incident to the car owner. All we could say is that the clairvoyant car owner is responsible for allowing Steve to exercise his free will and ultimately end in the killing of a pedestrian, maybe making the owner thoughtless or uncaring; aka negligent.
Is this necessary? Let's explore the notion. God created a universe of free creatures who He knew would sin. Does this make God responsible for the sins of His independent creatures? No! There are no philosophical or logical reasons to say that God is responsible for those sins. Mr. Swan's assertion that "If I knew in advance that a person was going to get in their car by their own choice, and while driving down the road strike and kill someone, and I let them do it, I share responsibility" falls short of holding merit. So in that the main point of the analogy is to show that Steve is responsible for the car accident, it fails.
Also, Steve's being negligent is of course not analogous to God's dealings with sin; God warned Adam and He warns us and we know He hates sin and does not desire the death of the wicked. Still, there lingers a sense in which it is not God's highest priority to prevent sin. And this is because He seeks a greater good which involves both granting man a certain amount of freedom and marvelously bringing good out of our sinful actions (see #1 below). Also, as we shall see, God is not a man, subject to the same obligations and duties that human beings are; he is the Sovereign Creator and Ruler of the universe (see #3 below).
Now if you are familiar with apologetics, Mr. Swan's scenario here looks very much like the skeptic's argument of the problem of evil. He even points this out in his post, "Many of you probably realize the above arguments are those typically launched by atheists against theists that use free will to absolve God of evil and determinism." That's correct, and should have tipped Mr. Swan off that this example doesn't show that God becomes responsible for all sins. All it could possibly show is that God would somehow be a bad guy for creating people who He knew would sin; that that act itself would be a sin. Of course we know this is silly, since God will not act contrary to His own law and thus will never sin.
There are numerous responses to the problem of evil, but first I want to point out an obvious logical problem that anyone who would question the libertarian runs into, and that is the Grandfather paradox. Since the libertarian believes that God foreknows actual future acts, then if God foreknows what a free creature will do in the future, he cannot not create that person, otherwise His foreknowledge of what the person will do would be wrong (since the person would not in fact do what God knew he would do; indeed, God's foreknowledge of the person's existence would be wrong as well!), and God cannot be wrong.. If you want to introduce middle knowledge (or whatever you may call God's hypothetical knowledge) then I would just point out, as a friend has done, that "God can only have middle knowledge...of people who will certainly exist at some point. He cannot know what someone who never exists would do; there is no person there to ever know anything about."
This list is by no means exhaustive, but it is enough to show that Mr. Swan (and by extension anyone who would cite the problem of evil) is incorrect in his assessment and that libertarianism (Arminianism in particular) is the Biblical view of God's foreknowledge and human freedom. I do not necessarily hold to all of these arguments I am going to cite, but will present them to show that Mr. Swan's line of reasoning is not necessary and that a libertarian has several options to choose from in refuting this argument.
1. Even if you reject the problems the grandfather paradox brings up, God still may have morally sufficient reasons to allow free will and have known the sin and have still created humanity. Let's apply this to the Mr. Smith car accident analogy. Say that I do know that Mr. Swan will have an accident and kill someone if I allow him to freely take my car. But perhaps I also foreknow that beyond the car accident there is an unspeakable good that will come about as a result of the car accident. Imagine that I knew the person he killed was going to try to kill the president. Would it still be wrong that I allowed him to take the car? It doesn't seem so. It seems that the reasoning behind my decision is morally sufficient to justify allowing Smith to take the car, resulting in the accident.
This is what libertarians could argue about God's decision to create free people He knew would sin. We could argue that God, in eternity past, decided to create creatures with libertarian free wills knowing they would sin in order to manifest a far greater good, namely the glorification of God! He knew He would save those who freely choose Him showing us His grace, mercy, righteousness, and love by redeeming us from those sins. I would argue He created the world in which the optimum amount of free creatures would freely choose Him.
2. One of God's main purposes in creating humanity was to cultivate a personal relationship with them. If He has determined all that we do, then the relationship is one sided, and therefore a sham much like a puppet show. It appears that for there to be genuine relations between people, it requires both parties to be able to choose not to be in the relationship. That could be the rationale behind God allowing freedom, and therefore the possibility of rebellion.
3. God is sovereign, and there is a demonstrable difference between our relationships with other created beings and God's relationship to us as Creator. Since He has sovereign rights over His creation, He has the right to create free agents, allow them to sin, and hold them responsible for those sins. So while it may be wrong for us to allow a helpless person to be murdered, it is not wrong for a maximally good and righteous God to allow His sinful creation to be killed, especially since He is their judge before and after they die (and since He has morally sufficient reasons to allow this sin as shown in #1).
I think this sufficiently shows that Mr. Swan is mistaken in his assessment. It shows that his analogy doesn't actually show what he wanted it to show, and the problem that seemed to arise in the form of the problem of evil isn't actually a problem at all for libertarian Arminians. But the determinist is still stuck with the problem in spades. If God has made necessary all events that happen, then sin is included and God actively causes sin. He becomes the active agent behind sins. The problem is still there and I don't think it can be resolved without holding to libertarianism.
Hopefully this "dilemma" will be put to rest among determinists.