Therefore, the best way to reason about the common political compass is that the vertical axis is authoritarianism vs libertarianism, and the horizontal axis is economic authoritarianism vs economic libertarianism.
It's not though. Your premise is not satisfied by definition because if someone were authoritarian then they would not be libertarian. It doesn't matter how people classify themselves, only their actual positions. A lot of libertarian socialism is about building cooperatives, unions, mutual aid, free banking, etc. You're just begging the question, assuming what you want to conclude.
> vertical axis is authoritarianism vs libertarianism, and the horizontal axis is economic authoritarianism vs economic libertarianism.
That's just nonsensically redundant and not useful.
Again, I'm not interested in having this conversation, so I won't be responding again.
Again, you're just begging the question and not giving any argument, despite being given counterexamples. No personal liberties are override by forming a cooperative.
No. Authoritarianism and Libertarianism are orthogonal to Left and Right in almost all modern models that include two or more dimensions [1][2]
1. https://en.wikipedia.org/wiki/Political_spectrum
2. https://www.politicalcompass.org/