I was watching Tony Evans this morning, and he had a great explanation for this. Though God desires all men to be saved, he doesn't force himself on anyone. I don't have the exact wording, but according to the message I heard this morning, God has his directive will and his will of desire. The desire allows each person to make the decision of whether to accept or reject Jesus Christ as savior, or something to this effect.
I like Evans. My son got to hear him speak this past year.
And he is right, although I am not sure about defitions insofar as desire or will.
The problem with not making a distinction between God's desire (His nature) and God's desire (His plan) is ultimaty one or another is lost.
Either men believe God will not punish sinners because His desire is good and holy (He does not desire evil, reign, etc) or God does not desire all men to be saved because His desire is good and holy (He desires justice).
But Scripture presents God as more, not less, complex than man. Scripture presents evil as not pleasing to God, although it exists.
The question for some is how can evil exist if God is sovereign without evil being pleasing to God as God can do all He pleases.
Evans answers the question very well.