The plane has crashed. People are seriously injured, but you are not. A stewardess, directing things, barks an order at you, “Go get the first aid kit from the overhead compartment!”. Intuitively, you are obligated to follow her order, due to her issuing it, even if it is not the best order she could have made (maybe the first order of business should have been finding water or finding the radio to call for help). In other words, something about the situation gives her authority over you (and the other passengers).
On Estlund’s “normative consent” theory (perhaps more aptly named “obligatory consent” theory) [DEMOCRATIC AUTHORITY, ch. 7] the salient thing is that, in this situation, you are morally obligated to consent to obey her orders if presented with the chance to do so. This is what explains your moral obligation to obey. That the chance was not presented or that you otherwise did not consent (perhaps even by actively refusing to consent) does not matter. This is a particular version of hypothetical consent theory.
However, it might be that what explains the authority here (your obligation to obey) is simply relevant items of normative significance (e.g., that certain important things will get done only if such command-following occurs) favoring your obedience. Perhaps these same things favoring your agreeing to obey does no work at all. In which case, we have what is sometimes called a “direct normative justification of authority” (or “direct theory of authority”). It is hard to sort out these different explanatory proposals because the considerations that favor obedience typically favor agreeing to obey as well (and vice versa).
But here is a fanciful (but hopefully still useful) case in which these two favoring relationships come apart. Picture a moral world in which one’s honor is among the very most morally important things and one’s honor is compromised fatally by agreeing to obey another person. But the causal efficacy of obedience in achieving morally important outcomes remains. If all of that were the case, it seems to me that one would still have compelling moral reason to obey the stewardess even though one does not have compelling reason to agree to obey her. So there would be authority.
This suggests that reasons favoring agreeing to obey are not what does the important explanatory work, but rather reasons favoring the obedience itself. And hence that Estlund’s normative consent version of hypothetical consent theory is wrong. This case suggests as well (and more broadly) that hypothetical consent is relevant only as a way of indicating the constellation of considerations that generally favor both agreeing to obey (consent) and obedience. Ideal consent or the normative favoring of agreeing to obey (consent) drop out of any fundamental normative explanation of authority.