Non-violence can be derived from any ethical position that views others as equal to yourself in all ways.
Actually, I don't think I agree with this. If everyone is equal and there are a limited amount of resources, why isn't everyone allowed to compete (or fight if necessary) for those resources? To the victor go the spoils? On the contrary, I think it is only when we have some sense of the dignity of the human person or a sense of self-sacrifice for another "equal" that we could hope for non-violence. Not all ethical positions contain a sense of this dignity. Certainly not all contain a sense of self-sacrifice. Ayn Rand's objectivism is all about self-interest. When the interests of the totally self-interested collide with one another, violence is possible and probable. What ethical systems teach self-sacrificial concern (or might I even proffer the word love) for others?
Evidence: Cats don't ask other cats for evidence of their dignity or debate the nature of it in public discussion forums.
Uncertain fortune is thoroughly mastered by the equity of the calculation. - Blaise Pascal