Example: I came downstairs to find Daniel on the ground crying. I had just asked the kids to clean up the den because Kyle was coming home and I ran upstairs for a quick pretty-up job. I asked Isaac what was wrong, and yes I was assuming Isaac was responsible for the crying. Isaac said: "I was putting away the Legos and Daniel really wanted to play with them. When I told him we had to clean up, he tried to bite me on the leg, so I pushed him down. (Now, I should mention that the area Daniel chose to bite was really close to a vital male organ. One that boys are born knowing should be protected.) I don't mess around when it comes to my future grandkids. Daniel was punished. And in this instance, Isaac was given only a talking to about better ways to elicit cooperation.
The job of a referee is to make sure the game is fair. Fairness is not my goal.
When one kid comes in crying: "She hit me!", my first question is always: "What did you do to make them want to hit you?" That almost always ends it. ;)