“Who gave him the 'authority' to do this?” “He didn't do it 'on his own authority' [=he didn't do it on his own]; he was acting 'under the authority of' the company president.” [=the company president gave him the power to do it]
No one 'in authority' objected to the plan. = No one 'in a position of authority' objected to the plan. [=no one with official power to make important decisions objected to the plan]
This office has 'authority' over personnel matters. [=this office has the power to make decisions about personnel matters]
(..) I don't think they'd ask you to stand, sire. Shirkers. Ingrates. Rabble-rousers. Who would have the nerve to question my authority? Who would dare? Who-? Bard. You mark my words: Get your hands off me. (..)2013 The Hobbit: The Desolation of Smaug