The way I see it, apart from free will, we are faced with accepting either Universalism or Limited Atonement...one or the other.
Because Irresistible Grace is a reality (1 Corinthians 13:8, Revelation 19:6).
And therefore, if God wills all to come to repentance and to be saved and come to the knowledge of the truth, then all will (see 2 Peter 3:9, 1 Timothy 2:3-4). Which indicates Universalism.
However, there is a hell, and certain people are going there (Matthew 13:41-42, Matthew 13:49-50, Matthew 25:46). Which indicates Limited Atonement.
But both can't be true at the same time; and the only answer I can think of to make it make any sense is free will and the fact that God's predestination is according to foreknowledge (Romans 8:29, 1 Peter 1:2).
God is Omnipotent and His love never fails; and therefore if there is anyone who does not enter the kingdom, either His love failed and He was not Omnipotent or else He didn't love them in the sense of choosing them from before the foundation of the world. Nevertheless God is not willing that any should perish.
The answer that my wife came up with to this inexplicable dilemna is that God in His sovereignty gave mankind a choice as to whether he would love God or reject Him...and then He chose the ones who would receive Him and predestinated them to salvation...like an author writing a book, who wants everyone to be the good guy and have a happy ending, but there would be no conflict in the story without a bad guy who gets defeated in the end...the author has a predetermined idea of how the story will go...in the midst of the story the characters make choices and may even surprise the author to make the outcome of the story slightly different than he originally thought in his planning out of the original story...
Or, it is like someone who looks at the outcome of a horse race, then goes back in time and bets on the horse that won the race.
God sovereignly choosing to give man a free choice is essential to the absence of a contradiction, if you will think on how these things are layed out.
With Irresistible Grace being a given, and the Lord wanting all men to be saved, it is Universalism apart from the concept of free will.
The fact of hell means Limited Atonement must be the reality except for the fact that Irresistible Grace + God wanting all men to be saved = Universalism.
But God can desire all men to be saved and His love cannot fail, and some people can go to hell (the reality that we see in scripture); if God in His sovereignty and love gave man a free choice in the matter of whether he will go to heaven.
In this scenario, God's love does not fail to give man a choice as to where he wants to go in eternity...but His love does not fail (and neither does His Omnipotence) even though some will not make it to heaven because they chose to go elsewhere.
Because, again, if God's love does not fail to bring a man to heaven, and God loves everyone (wanting them to be saved) then apart from free will you have Universalism...however it is clear from scripture that some will not be saved...and this cannot = Limited Atonement because God is not willing that any should perish.
So then, some (and not all) are saved through sovereign election, but this election is according to God's foreknowledge of whether they will choose to receive the gospel of their salvation and surrender to the Lordship of Jesus Christ.
For if man does not have a choice, then His going to hell means that God did not love him and wanted him to go to hell (since He is Omnipotent and His love never fails) otherwise lack of free choice means that all will go to heaven (which is not what the scripture teaches).
Therefore man having a free choice in the matter is the only option that is left.
Of course no one can come to Jesus unless the heavenly Father draws them.
So I would think that God draws every person at a specific time in their lives and they make their decision; the drawing effect of the Holy Spirit enables them to make a choice that is unhindered by outside forces.