Is the idea that moral behaviors must be based on standards of equity, fairness, and impartiality to preserve order in society?

I believe the correct answer is Justice.

Justice general concept is fairness in the way that people are treated and fairness in protection of rights and punishment of wrongs. However, as with most philosophically-driven disciplines, the concept of justice differs in every culture. As a vague example, for some cultures, when a woman cheats on her husband, she has to be physically punished, while in other cultures she is probably only socially judged; the concept of justice here has different implications.