I don’t believe that an authority has anymore right to do this than an ordinary person. An authority is a flawed human like all of us. What makes him an authority?
Discussion
I believe in a few but still legitimate positions of authority. Their authority flow from and they are responsible to the ultimate authority, who is God. I'd say a father has a similar although much broader kind of natural authority.
Functionally, I'd say governments should administer justice because ppl avenging themselves can lead to escalations of violence and some victims are too weak to avenge themselves.