Drawing on an account of satisfaction theories recently set out by Oliver Crisp, I argue that all theories of atonement which specifically relate Christ’s suffering and death to satisfying divine retributive justice, are forms of penal theory. I introduce the notion of satisfaction-penal theories. I compare their structure to penal substitution accounts. In both, the appeal to the dignity of the Son of God is critical. A key underlying difference is what is offered to God: Christ offering himself, in perfect love and obedience, or the value of the punishment borne by him.
Rolfe King (2025) studied this question.