A president exercises authority with respect to a group that includes herself. She is included in two ways. First, the common good that her authority promotes is a good of a group that includes herself. Second, her legal enactments bind her just as much as they bind other citizens.
Not all authority is like this. A Dean of Students, for instance, exercises authority over students and for the sake of their good, and typically is not a student herself.
Sometimes authority of the second sort derives from authority of the first sort. The Dean of Students has an authority deriving from the consent of the students, and the students have an authority of the first sort over themselves. The general has an authority of the second sort (I think), deriving from that of the president.
An interesting hypothesis is that the second sort of authority always derives from the first. There are two nice test cases: parental and divine authority.
Parental authority is of the second sort. Is it derivative? If not, then the hypothesis is false. Maybe parental authority derives from the authority of one or both parents over the whole family, which would be of the first type? Or from God's authority?
God's authority is surely non-derivative and yet seems to be of the second type, yielding a counterexample. But maybe God's authority is of the second type: God is trying to put together a kingdom of ends that he is head of.
Or maybe the first sort of authority derives from the second? That could make for a neat story, with divine authority on top.
Or maybe there is no interesting derivation relationship.