Usually I like Andrew Sullivan, but his approval of this schematic disturbs me:
Only a non-scientist could come up with a taxonomy like this. We have six distinct categories and only one degree of freedom (angle); for reality to really parse like this requires an explanation.
(One could say the same for the color wheel, and in fact, I do. The psychology of color perception is a baffling business... But it happens we can see just about an octave of light which helps a bit.)
It reminds me in some vague qualitative way of Roger Pielke Jr.'s double taxonomy of scientific types, in which he obtains precisely the identical decomposition using two drastically different tactics. I'm reasonably convinced he made some effort to understand my critique but didn't manage it.
So the convenient symmetries of Sullivan's graph (no such thing as a corrupt libertarian, then?) just don't have the ring of truth. What's more, this completely misses what I consider the fundamental determinant of politics, the question I ask first, which is how much the respondent considers politics a managerial question in a quantitative physical domain. Whether such issues as energy, climate, demographics, ecosystem stability, ocean chemistry, trace toxins, and bulk trash enter into your model or not is to me the dominant question. I don't care if your solutions are "conservative" or "liberal" so much as I care whether your idea of politics addresses the fundamental engineering questions raised by a large population on a small planet.
The fact is that most participants in politics from most parties are uninterested in these matters. This makes most politicians woefully incompetent. The left-right dichotomy will not go away, and making it into a hexagon or the more familiar and more plausible two-factor spectrum (public sector and private sector "liberty")doesn't help.
The main issue right now is whether you see governance as a quantitative problem.