“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]
(..) - No, Bill, l... - You guys stay here. There's no sense in everyone getting drenched. TV reporter: Returning to the news, local authorities still have no lead in the mysterious disappearance of the five cheerleaders from Ruggsville. The girls were last seen leaving a cheering competition... (..)2003 House of 1000 Corpses