A clear and detailed political typology can be inferred from Fiske’s Social Relations theory giving us a view as to what is the difference between between rightist anti-democrats and the democratic right and also the differences within the democratic right. This spectrum is mirrored on the left and we have an explanation for outliers such as the Greens and the Libertarians.
See the extreme right here, focused on CS and AR contemptuous of EM and broadly indifferent to MP. These latter two points are what most clearly cleaves them from democratic right.
We can see four types of democratic rightists outlined below, all weaker in emphasis then any leftist on CS, all strong on EM and MP. It is the strength of the MP reference which distinguishes the Free Market Conservatives and Libertarians from the other two types. These two types cannot balance solidarity with prosperity as in the German Social Market economy of Angela Merkel because MP is too deeply moral, the sanctity of private contract allied to individual initiative cannot be balanced by social requirements because CS is too weakly felt. Note that the Libertarians are virtually only playing with one club here and one club from Haidt also – Freedom To (negative liberty). The iron political rule would be that more extensive your reference to Fiske’s social models the greater your appeal.
Four types of leftists here, although left authoritarianism is rare given the association of the left with reverse dominance. As noted above the far left eschews AR in principle but requires its operation in practice if the revolution of the proletariat is to concur all society and defeat its enemies. An interesting new split is between traditional social democracy and the emerging pro-market left. The distinction is in the pro-market left’s acceptance or enthusiasm for MP methods and principles.
Famously the political spectrum was held to be oddly circular with lives lived under the Nazis and Soviet Communists dominated with demands of the collective and requirement to obey and actively support in-group authority. The picture below show why this is: both left and right referencing CS and AR very strongly.
Some of the other ideologies are worth looking at, the moderate Nationalists shade to the right and look like Christian Democrats. The definition of a classical British Liberal is the intense valorization of EM – democracy, rights, constitutional structures. The Greens are weak on EM and MP, have no AR (probably reverse dominant) but according to Ravi Iyer who researched the Haidtian structure of environmentalist thought found them like leftists so here they are strong on CS.