Here's my new way, please comment.
But first a critique of the old system and why I find it doesn't work.
The current alignment system in D&D doesn't make sense to me, such as evil, pure evil or chaotic evil. Why would a being, by its nature, be evil? Why destroy stuff? What being in our world destroys for no reason? To destroy what one considers pointless or alienating, part of an oppressive system, doesn't make someone evil. I feel that often, the portrayal of evil in D&D has no overarching philosophy, other than world-domination. Or evil bad guys want to introduce extra-planar creatures onto the material plane so it will be "utterly destroyed." It makes no sense.
So evil doesn't exist. Sort of. What does exist is competing agendas and philosophies that provoke different biases, prejudices, and stereotypes. One man's Terrorist is another's Freedom Fighter. Were the Sons of Liberty terrorists?
I do like the axis though, and use it to explain Motivation, or Bias. Call it what you want.
Along the horizontal axis (the X-axis) is a spectrum, a political spectrum, I guess, with degree of regulation as its topic. It asks, "to what degree should the government regulate political, social, and cultural freedoms?" Heavily regulated on the left and unregulated on the right.
The Y-axis concerns the individual, and asks, "What is a person's chief motivation: the individual or the group?" Selfish-ism on the bottom and Altruism on the bottom.
So. If you are in the top left corner you would be someone who wants a lot of regulation and believe people are mostly for the group, putting others before themselves. I think the D&D would call a person in this box LG-ish.
And if you are in the bottom right corner, you want very little regulation, and expect people to be motivated by themselves. Would this be between CN and CE?
How about the bottom left corner? You want high regulations and believe people are selfish. Is there a match for this in the D&D? I don't think so. Is there a person like this in the world? Yeah, maybe the fear of others' selfishness motivates the government to regulate? I'm not sure.
And the top right corner leaves you with a person who wants unregulated societies and people who are mostly into the group. Anarchists? Local people in small groups who set the rules for themselves.
Here ends the first draft.