“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]
(..) TONY: Panama. You're Iooking for a partner, right? Something Iike that. Look, Mr. Sosa, we're getting ahead of ourseIves. I am down on Frank's authority to buy keys, that's it. That's my Iimit. I got no right. -Nobody got no right to negotiate-- -Let the man finish, okay? Let him propose a proposition, then we can taIk more. You got no authority here. I started you in this business, so shut the f$ck up. -Frank is gonna Iove it. -That's up to Frank, not you! I'm sorry about this, Mr. Sosa. (..)1983 Scarface