The political compass does more damage than it helps, ultimately. Left vs right is usually about collectivization of some form vs private ownership, but things get weird when you get to “libertarian vs authoritarian.” Neither of those really mean anything when the size of the state is related to the class character of society, the size of state isn’t really something people pick so much as it is something that is shaped by the mode of production.

Differences among the left and right are far more nuanced and can’t be distilled into “libertarian” vs “authoritarian.”