I teach my children primarily to fix things by righting the wrong. I fully realize that not all wrongs can be righted, but it is a valuable starting point. So many times I've had the pleasure of seeing my children come up with genuinely ingenious ways to right a wrong.
In disputes where I'm playing referee between two of my children, I gravitate away from deciding who is right and who is wrong. Instead direct conversation around, what happened, what people need, and how we can satisfy those needs within the creative realm of reasonable possibility.
As a baseline for issues that don't have a clear needs-based line to follow, I consider the systemic issues involved and re-engineer systems to incentivize good behavior and disincentivize bad behavior. Most often this takes the form of natural consequences.
Finally, I don't have angelic children. The reason it works is because we've been doing it for years, not because my children are more compliant, or I'm some saint. We all get upset, angry, and do things we regret. What we are all invested in is having a shared desire to make things better than we found them.
What I am skeptical of, however, are responses which attempt to frame children as willfully non-compliant. That says more about the person describing the behavior than the behavior itself.