According to Bavinck ( Reformed Dogmatics: Abridged in One Volume , 442-3), vicarious satisfaction means that Christ gives to God all that He demands from us, which we are incapable of giving: “The demand posed by God to fallen humanity was twofold: one, that humans would keep the law perfectly, and two, that they would redress the violation of it by punishment. The benefits Christ obtained for us are twofold: to bear our punishment and to obtain for us the righteousness and life Adam had to secure by his obedience . . . . It was the single work that Christ accomplished, but one so rich, so valuable in the eyes of God, that the righteousness of God was completely satisfied by it, all the demands of the law were fully met by it, and the whole of (our) eternal salvation was secured by it.”
Though Anselm’s name is often invoked in discussions of this theory of the atonement, Anselm doesn’t fit.
For Anselm, it is the fact that Christ’s death is unrequired that is the hinge of the atonement. Every creature already owes all to God; humans have failed to pay God His due, and there is a chasm between what God demands and what we can give; giving everything back won’t fill the gap, since everything is already owed; satisfaction requires more than everything. It requires a gift that is not owed.
Anselm writes ( Cur deus homo , 2.11): For Christ to give His life “is not something which God will demand from him in repayment of a debt, given that, since there will be no sin in him, he will be under no obligation to die.” No greater gift can be given than that a “man may suffer - voluntarily and without owing repayment of a debt - more painful or more difficult than death. And there is no act of self-giving whereby a man may give himself to God greater than when he hands himself over to death for God’s glory.” Christ’s gift in death is the greatest good, and thus (2.14) the debt of sin is paid. His self-gift in death is so lovable that it “can suffice o pay the debt which is owed for the sins of the whole world.”
Since this gift surpasses everything in value, and was voluntarily paid by one who did not owe the gift, the Father rewards the Son. Since the Son has everything already, He wills that the reward by given to others, namely, those for whom He died: “whom is he with greater justice to make heirs of the recompense due to him, and of the overflowing of his bounty, than those who are parents and brothers to him, whom he sees, bound by so many and such enormous debts, wasting away with deprivation in the depths of misery? The debt that they owe for their sins would, as a result, be excused and they would be given what, because of their sins, they are deprived of” (2.19). This makes little sense if Christ’s death is satisfaction of a debt in a direct way; after all, who gets a reward for repaying a debt? Since the gift Christ offered is unowed, undemanded, and infinitely valuable, it it fitting that it be rewarded, and it is fitting that the reward be shared as Christ wishes.
David Hart is correct: Anselm’s theory turns on the death of Christ not as the gift that repays a debt but rather as the “gift that exceeds every debt.”