I am transcribing the following directly from Barth on his doctrine of election. This is the clearest word you will get from him on what his reformulated doctrine of election entails. What you should notice is how it thinks from the patristic homoousion in patterned ways.
THE ELECTION OF JESUS CHRIST
The election of grace is the eternal beginning of all the ways and works of God in Jesus Christ. In Jesus Christ God in His free grace determines Himself for sinful man and sinful man for Himself. He therefore takes upon Himself the rejection of man with all its consequences, and elects man to participation in His own glory.
1. JESUS CHRIST, ELECTING AND ELECTED
Between God and man there stands the person of Jesus Christ, Himself God and Himself man, and so mediating between the two. In Him God reveals Himself to man. In Him man sees and knows God. In Him God stands before man and man stands before God, and is the eternal will of God, and the eternal ordination of man in accordance with this will. In Him God’s plan for man is disclosed, God’s judgment on man fulfilled, God’s deliverance of man accomplished, God’s gift to man present in fulness, God’s claim and promise to man declared. In Him God has joined Himself to man. And so man exists for His sake. It is by Him, Jesus Christ, and for Him and to Him, that the universe is created as a theatre for God’s dealings with man and man’s dealings with God. The being of God is His being, and similarly the being of man is originally His being. And there is nothing that is not from Him and by Him and to Him. He is the Word of God in whose truth everything is disclosed and whose truth cannot be over-reached or conditioned by any other word. He is the decree of God behind and above which there can be no earlier or higher decree and beside which there can be no other, since all others serve only the fulfillment of this decree. He is the beginning of God before which there is no other beginning apart from that of God within Himself. Except, then, for God Himself, nothing can derive from any other source or look back to any other starting-point. He is the election of God before which and without which and beside which God cannot make any other choices. Before Him and without Him and beside Him God does not, then, elect or will anything. And He is the election (and on that account the beginning and the decree and the Word) of the free grace of God. For it is God’s free grace that in Him He elects to be man and to have dealings with man and to join Himself to man. He, Jesus Christ, is the free grace of God as not content simply to remain identical with the inward and eternal being of God, but operating ad extra in the ways and works of God. And for this reason, before Him and above Him and beside Him and apart from Him there is no election, no beginning, no decree, no Word of God. Free grace is the only basis and meaning of all God’s ways and works ad extra. For what extra is there that the ways and works could serve, or necessitate, or evoke? There is no extra except that which is first willed and posited by God in the presupposing of all His ways and works. There is no extra except that which has its basis and meaning as such in the divine election of grace. But Jesus Christ is Himself the divine election of grace. For this reason He is God’s Word, God’s decree and God’s beginning. He is so all-inclusively, comprehending absolutely within Himself all things and everything, enclosing within Himself the autonomy of all other words, decrees and beginnings.1
So let it be written, so let it be done.
1 Karl Barth, Church Dogmatics II/2 §32-33: Study Edition (New York, New York: T&T Clark, 2010), 99-100.