The big picture,
The question is rather what is His Elect.
God's Elect refers to how God foresaw with His foreknowledge that who are eligible to live an eternity with Him, based on how freewill works. He knew before hand who shall be saved. He knew before hand who is who. He knew who each of us is by our very nature that whether each of us can or cannot live an eternity with Him. Thus He wrote our ID in the Book of Life of the Lamb.
However it's not legitimate for God save anyone at will, or else Jesus is not required. Jesus is a must for redemption simply because God can't legitimately save at will. If a ruler can save at will, it only means that his realm is a lawless realm. You can imagine that if your city mayor can grant a pardon to any criminal at will, it only says that your city is lawless realm.
God thus needs to set a standard in order to identify or qualify with this standard to save anyone at all. This standard (applicable to humans only but not the angels) is commonly referred to as a covenant. In a nutshell, earth is for God to show that His Elect is the qualified, openly under witnessing (of the angels and chosen saints such as Moses).
John 5:45 (NIV2011)
But do not think I will accuse you before the Father. Your accuser is Moses, on whom your hopes are set.
Moses is not sleeping in grave, he's keeping an eye all the times. (so is Satan)
Revelation 12:10 (NIV2011)
Then I heard a loud voice in heaven say: “Now have come the salvation and the power and the kingdom of our God, and the authority of his Messiah. For the accuser of our brothers and sisters, who accuses them before our God day and night, has been hurled down.
On earth, humans' freewill are to be fully exercised to demonstrate who they actually are. It is much easier for the unsaved or wicked to show who they are. It is however difficult in a wicked world for the righteous to demonstrate to be the righteous. The righteous also sin on earth. Predestination is to provide a fate to the righteous such that they can be fully demonstrated as the qualified in their short life in a wicked world. To put it another way, without predestination, it's difficult or even impossible to distinguish the righteous from the wicked, or the saved from the unsaved. Predestination facilitates critical choices made by a freewill, such that a human can be fully demonstrated who he is. He thus can be judged by the covenant he is subject to.
Jesus' crucifixion simply made a covenant (including each and every covenant ever granted in the history of humanity) to be a possible and legitimate way of judging humans. Without a covenant in place, every human will have to be judged by God's absolute Law (which applies to angels all the times) thus not a single human is savable in this case. By the judgment of this absolute set of Law, some angels will be qualified, angels are living in the realm of God. When this same set of Law applies to humans no one can pass, as humans are literally living in a realm whether Satan can be referred to as the god of this world.
In effect, Jesus' crucifixion regained the right of judgment from the hands of the Law. This actually makes Him able to "grant a pardon to any criminal". However this is not done at will but by paying a dear price. Now Jesus Christ and God can legitimately grant such a pardon to anyone Jesus sees fit. We trust that He's a fair God to do so. This can be seen as a subjective judgment by Jesus Christ. Those disqualified (i.e., the unsaved or wicked) now can be judged by Law alone. It is now an objective judgment where no humans are expected to pass. The Final Judgment is two-layered, that is, a judgment of covenant followed by the judgment of God's absolute Law, with the saved exempted from the latter.
