Parents have the authority to command their children and parents have a special duty to care for children. Officers have special duties of care for those under their command. The state likewise has special duties of care for those under its jurisdiction. Special duties of care do not imply authority: adult siblings have special duties of care to one another but do not have jurisdiction over one another. But we can hypothesize that authority implies special duties of care.
Why would that be so? One possibility is that authority always arises out of special duties of care: in some cases, in order to properly care for y one must have authority over y. That fits neatly with the parent-child case, but doesn't fit with the military case, where the authority seems explanatory of the duties of care, or at least not posterior to it. But in the military case we might say this: in paradigmatic cases (putting to one side the case of mercenaries), the officer's authority derives from the state's authority. And the state's authority may well arise out of special duties of care for its citizens, whom the state can thus induct, voluntarily or not, into the military.
This more general pattern can fit cases which don't fit the simple version of the authority-care hypothesis. For instance, perhaps, a judge has commanding authority over a convicted prisoner but does not have special duties of care for the prisoner. But the judge's authority derives from the state's authority, which is explained by the state's special duties towards its citizens. So the more refined hypothesis is something like this: The authority to command is connected with special duties of care, but the special duties of care need not be had by the one who has the authority to command--the authority to command may have been deputized from another who had both the authority and the special duties.
But what about this case: Sometimes a state will imprison those who are not under its care but who have harmed its citizens. One example is prisoners of war. Another is the case of seizing a criminal from another country, as in the case of Manuel Noriega. I could wimpily say that the hypothesis is just a general rule with exceptions. But perhaps what I should instead say is that the case of prisoners of war and criminals seized from abroad is not a case of authority to command and hence no exception to the hypothesis. While an imprisoned citizen does violate duties of obedience to the state in escaping, the prisoner of war or criminal seized from abroad do not violate any such duties of obedience in escaping. There may be a limited commanding authority, however, derived from duties of care. Thus, an officer in charge of a prisoner of war camp might have commanding authority in respect of keeping order at food lines. And in even other cases there may be moral reasons to obey not because of authority but in order to maintain order, which is good in itself.
So let's suppose the hypothesis is correct. We now come to two of the most interesting cases: God and self. If the hypothesis is true, then God's absolute commanding authority over us derives from God's duty to love us. That's surprising, but may be right. The case of self is even more interesting. While we may not, strictly speaking, have commanding authority over ourselves (though "promises to self" might be an example), the authority we have over ourselves goes beyond most cases of commanding authority. Does that authority, too, derive from duties to care for ourselves? I like that idea, but many will not like the idea of duties to care for ourselves.