to clarify:
The authoritarian/libertarian axis refers to social and civil policies (and perhaps to sone extent democratic freedom.) It makes more sense of you just see it as "socially conservative" and "socially liberal, " excluding economic policies, which are the left/right axis. American libertarianism would be the purple quadrant, republicanism the blue quadrant, communism the red quadrant, and American democrats (social democracy/greens) the green quadrant.