These views aren’t complicated though, or aren’t as complicated as you think. Most of our political opinions can be boiled down to any of the 4 quadrants of the axis.
Can you name any view that doesn’t fit into this axis?
Many. Which is more “authoritarian” and which is more “libertarian,” a fully publicly owned and democratically controlled economy, or a highly decentralized market economy with a nightwatchman state?
Well it depends right, let’s not act like there isn’t nuance to this.
a fully publicly owned and democratically controlled economy
It falls on the libertarian-left if individuals and communities genuinely govern themselves without coercion e.g democratic socialism. However, if the system requires a strong central authority to enforce public ownership and suppress alternative systems, it moves toward the authoritarian-left e.g Marxist-Leninism
a highly decentralized market economy with a nightwatchman state
This is just a straight up libertarian right economy. A nightwatchman state equals laissez-faire capitalism which aligns with libertarian-right philosophy.
To answer your question, it depends on the type of publicly owned and democratically controlled economy we’re talking about.
See, this is where your analogy falls apart. Marxist-Leninists support recall elections and more democratic methods than what you describe as “democratic socialism.” You’re trying to add to the existing example to make it mean something it doesn’t, I asked you a straightforward question and you had to add to it in order to force it into your tidy and neat boxes.
Same with what you call “lib-right,” I would consider that more “authoritarian” because people have far less actual control over their lives than they would in the other example, despite focusing on decentralization. In such an economy, warlordism would be the dominant factor in decision making.
This is why the Political Compass is an exercise in absurdity, you cannot simplify viewpoints to 4 quadrants because that’s not how economics or politics actually works. You can only describe them by their real and existing mechanisms.