That's a fantastic question, and the short answer is: "given my expertise is in the Theravada world... how authority works is complicated". An overly simplistic answer is: the number of years of a monk's seniority is the easy and fairly-reliable gauge of a monk's authority.
It would take a good 1-hour Dhamma Talk for me to explain what I know. Most people would be bored, and possibly even uninspired after hearing the non-tldr answer. Do you really want the non-tldr answer?