The atonement doesn’t take place “above the heads” of the participants – Jews, disciples, Pilate, Jesus – but in and through their concrete actions and reactions. There can be no sociology of atonement unless the atonement is understood as an inherently social and political event.
On the other hand, modern alternatives to satisfaction theory are efforts to formulate a “merely social” understanding of atonement. They work on this premise: If we leave God out of the event of the cross, how does Jesus’ death have a saving effect? “Moral influence” and “governmental” theories are, or at least can be, merely social atonement theories.
The deepest flaw of such theories is their secular assumption that there can be such a thing as a “merely social” event.