There are Scriptures that indicate the offer of salvation is universal and without prejudice; 2 Peter 3:9, Romans 12:3 are just a few of these.
Let me use our electorial process as an example. In November American's will go to the polls to elect a President. We choose who we will vote for based on their record and philosophy of government. The doctrine of election can be viewed in the same manner. God elects those who demonstrate in their lives, hearts, and minds they fully believe and accept His sovereignty. Then those who He elects based on their free will decision are then predestined to perform good works and live under His sovereign will.