Does God have two wills?

If it is true that the Bible teaches that God unconditionally (i.e. not on the basis of foreseen faith) chooses those who are to be saved, and it does, does the Bible contradict itself when it says that God ‘desires all men to be saved and to come to the knowledge of the truth’ (1 Timothy 2:4)?

Put another way, if God really desires all men to be saved, why does He only choose some of them actually to be saved, while eternally condemning others?

In his article, Are There Two Wills in God? John Piper addresses this apparent problem head-on. He gives a cogent and coherent Bible-based explanation of how divine election and God’s desire for all to be saved are two harmonious and consistent truths.