A formal order given by a higher authority is called a mandate. This can be an order given by a higher court or a person in higher power within the government.
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Actual authority
Police Power
its a hammer. used by judges or presidents to close session: the final word
Acknowledging British authority helped keep social order on the boat.
Someone who uses their authority to order others to do something small or unimportant, mostly for the purpose of demonstrating to that other person that the person in authority is in fact in a position of authority. E.g. "I'm the one who decides whether you do or do not enter this room. So if you want to go in, you'll have to . . . put your hands on your head and say 'Moo'. "