Left - Right
Authoritarian Left + Right Libertarian
This seems nicer, but I suspect creates a false distinction. There's not much practical difference between an authoritarian left and an authoritarian right, it's still just a few people in charge. I instead propose a triangular model:
Hierarchy Individualism Communism
A society is composed of a mixture of these three forms of decision making. WWII saw a fight between pure-hierarchy and everyone else, which was followed by an extended argument over the merits of a highly individualist society versus a mixture of hierarchy and communism (heavy on the hierarchy).
It should be noted that although a communist society has been a goal of a lot of a people for at least several thousand years, no one knows how to do it in practice. There is universal lip-service paid to its desirability. It may require a change in human nature, on which point there has been slow but real progress over the past few millennia. Maybe computer networks will help.
Why this matters: We're looking to shoot straight on past the 4-degrees warming scenario. This is very, very bad. In highly hierarchical societies (China), the rulers are unwilling to act to stop this -- better to maintain a hierarchy in hell, genuinely better for everyone is the belief -- whereas in highly individualist societies externalities tend to be under-valued. Our oligarchical west gets a double dose of suicidal tendency here.
There is an argument in the green faction to say "never mind all this social justice stuff, we need to concentrate on global warming.". It's worth meditating for a moment on the scale of horror of this strategic idea (if it helps, imagine it somewhere else on a smaller scale). However, even if we accept that the misery that will be caused by climate change outweighs the misery caused by endless social injustice, which I tentatively accept, I think this is a mistake. While we still live in a world of sexism and class divides, progress will be nearly impossible. Enough!