Not To Be Confused With
Anselm's satisfaction (honor/justice owed to God) is the medieval forerunner of penal substitution but frames the debt as honor and fittingness rather than penalty borne. Both differ from the moral-influence view, which locates the effect chiefly in us.
From Anselm's Cur Deus Homo (“Why God Became Man,” c. 1098): humanity owes a debt of honor it cannot pay, and God will not simply waive justice; the God-man alone can both owe it (as man) and pay it infinitely (as God). The theory reshaped Western atonement thought.