supervision

this is about the one who can see things others cannot in a given context or situation.  It is not the same as authority or responsibility.

Responsibility lies with the one who has the Super vision, for only they can See that the others cannot.  It is simply a matter of whether they have the personal authority to exercise what they See, or not.

Parenting is a great example of where things get confused over these terms.  Healthy parenting is Supervision, unhealthy is authority.  Response ability determines the result