When Calvinists use phrases like God does not desire man to sin, but he does permit sin, it is easy to misconstrue their meaning of the word permit and understand it in the libertarian sense.  The libertarian understanding, which is the normal way the word is used and understood, would simply mean God created Adam and Eve so that they could choose not to sin, and that is what God actually desired for them to do even though He permitted (allowed) them to sin if they so chose; the same is true with people today.
However, in Calvinism, God endowed man with compatible moral freedom, thereby predetermining that man would freely choose to sin. Compatibilism means that man is considered to make a free choice when he chooses according to his greatest desire. What often goes unstated is that while the choice is free, the desire from which it flows is determined by his past or nature; thus, it is precisely accurate to say, according to Calvinism, man makes a predetermined free choice.
In Calvinism, according to their commitment to compatibilism, God could have created man with a different past or nature, thereby predetermining that man would always choose holiness and man would never sin. However, it did not please God to spare man the torture of sin and, for most, an eternity in hell; therefore, he predetermined that man would freely choose to sin. Consequently, that he permitted man to choose to sin simply means God predestined him to freely choose to sin, but that freedom does not include the possibility of choosing not to sin.
To state it another way (according to Calvinism and its belief in compatible moral freedom), God could have just as easily created Adam and Eve with different natures, emanating different desires, thereby determining that they would have freely chosen not to sin; as a result, sin would not have entered into the world. This would have resulted in a world without rape, abuse, death, murder, and every other nefarious sinful thought or act, including people spending eternity in hell, but such a world God did not desire, according to Calvinism. Therefore, it is undeniable that the presence of sin and every vile, sinful, and hurtful act by one of God’s created beings pleases him according to Calvinism in a way that is not true of Extensivism (non-Calvinism).
Although from a libertarian perspective as is presented in Scripture, this does not make sense, it is quite reflective of compatible moral freedom. Once more, we see the ever-present calvinistically generated quandary, which is that God must not only have desired to create man but also desired to create man to predeterminately freely choose to sin. This explanation is the precise meaning of compatibilism; consequently, it does not make the error of saying God caused man to sin or that God does not employ secondary causes. It simply explains the very nature of compatibilism and, therefore, the presence of sin.
According to compatibilism, man freely chose according to his greatest desire and is, therefore, responsible. Of course, this raises the question of ultimate responsibility since man’s desire was determined by his past and nature, which God gave; accordingly, God is ultimately responsible. That is to say, man is the proximate cause of his sin, but God is always, according to compatible moral freedom, the ultimate cause.
In contrast, Extensivists believe in libertarian freedom, which means that man is both the proximate and ultimate cause of his own sin. Thus, as a holy and merciful God, God genuinely desires that no one would choose to sin and perish in hell, but He permits people to choose. Therefore, when Calvinists use the word permit, it is no less deterministic than any other event within Calvinism.
In future articles, we will look at particular Calvinists like D.A Carson and Paul Helm’s unsuccessful attempts to relieve God of the ultimate responsibility for sin.
 Libertarianism: man is not determined, and his Creator endowed him with the ability to choose between accessible options in most situations. Libertarians contend that determinism is not compatible with moral responsibility. When God or man overrides a person’s free will, the person is not responsible for that particular choice, but he does not lose his free will.
Man possesses actual otherwise choice and can therefore act or refrain within the God-given range of options. Adam’s range of options before the fall was greater than humanity’s options after the fall. The range of options present before the fall was the result of creative grace. The range of options present after the fall is the result of redemptive grace.
Compatibilism: compatibilism says that 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 that as long as a person chooses according to his greatest desire, he can be considered to have 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. That is to say, his nature and past determine his greatest desire; thus, his free choice is actually a determined free choice.
For a complete explanation of the definitions and differences between Libertarianism and Compatibilism, search Compatible and Libertarian Freedom at ronniewrogers.com. A more current explanation is in my book Does God Love ALL or Some? Comparing Biblical Extensivism and Calvinism’s Exclusivism
 Extensivism is the term I use to broadly include perspectives that reject Calvinism and believe that God salvationally loves and provisioned for everyone to have an opportunity to believe the gospel and be saved.