For the sake of discussion, "authoritarian" vs. "libertarian" is a useful concept. But that compass still uses the utterly useless 'left' and 'right' dimensions.
One axis represents the economic and the other the social dimension. No ambiguity about left and right there. It's obviously only a model and people's actual political beliefs have more dimensions.
The words "left" and "right" can be used in an economic sense. In terms of actual political usage, the definition of left and right varies so wildly among individuals that it has no one understood meaning.
It’s not that interesting, left and right is still on a single line, the 2nd axis only represents how pushy they are. People’s politics are way more complex than this.