Who may carry out protective deterrence?

Anthony Ellis argues that institutional punishment occurs automatically in a way analogous to mechanical deterrents, and given that issuing real threats is justified for self-defence, institutional punishment, intended to protect society via deterrence, can be justified without violating the Kantian constraint against using persons as means only. But institutional punishments are not in fact executed automatically: they must be carried out by moral agents. Ellis fails to provide a basis for those agents to justify the performance of their legal duties.