Even that doesn't really work. A libertarian is someone who's based their political ideas on a flawed understanding of economics. Authoritarianism is just a scam that convinces people they should be ruled over by someone that will [make their country strong/make them more equal/protect them from whoever they're afraid of]. It just further legitimizes ideas based on a flawed understanding of the world and invents new issues just to have things to slot onto the graph.

Like how do you feel about "late stage" capitalism? How do you feel about bad people eating people's pets? I can point at government inefficiencies to prove that the government should be eliminated so we can all live in a libertarian utopia. And we can plot these things on a page, and legitimize them as real ideologies. But really they're just things people have made up or have exaggerated to push people away from solving the problems towards "ideologies" that need those problems to exist to justify their existence.

A large part of politics is about perception. We have a fairly good understanding of how the economy works. We also have a good idea understanding of how the climate works too. Biden actually did extremely well on the economy. But the perception is that he was terrible on the economy issue. There's a lack of understanding of how things work and so we end up with the idea that voting in a Republican will make the economy better because they're going to drill for more oil. The right of the spectrum is good on the economy and the left of the spectrum is bad on the economy, everyone knows that! But really this spectrum thing just allows people to exploit perceptions and calcify those perceptions.