While reading the latest Red Lanterns (#3, Nov 2011) the leader of the Red Lantern Corps says that he wants to bring vengance to those who have caused people hatred and rage. He seems to want, when you get to his core, to help people and punish those that have caused harm to the innocent.
Why is it then? From what I know about the other rings (except for Orange since there is only 1), all the rings are at the base of it all, trying to bring order and justice to those who can't do it for themselves, with the exception of the Yellow rings.
Why don't the Yellow Lanterns also want to bring justice and order to the Universe? It seems that only Sinestro wants this goal, but the other YL's only want to bring fear to the hearts of everyone in the universe.