The way I see it, is that they are not exactly the same, but there seems to be a greater tendency in the "up-directed" people to be also right-leaning, also a greater tendency in the "down-directed" people to be also left-leaning, which makes sense, since many elements in those pairs of tendencies/ideologies almost line up, or are at least very compatible.

However, there IS also right libertarianism, and left authoritarianism, but those seem to be less probable than the opposites.

Take a look at the Political Compass mappings of famous politicians and political parties in different parts of the world: The up-right and down-left quadrants are almost always the most populous, while there are dots in the other two quadrants.

(See the "Elections" section on the left column, click on several elections in different locations.)