I think I am understanding something incorrectly in Optimality Theory but I can't figure out how. So, constraints are universal but rankings are language-specific. So, I read an analysis where they ranked one constraint higher over the others in a particular language. Then they did the factorial typology, and after they got all the t-orders, they said that the typological entailments are implicational universals. I don't understand why these are called universals, when they were calculated with a language-specific ranking. What am I understanding wrongly? I would appreciate any help, thank you.
A "universal" in their sense refers to the possible input-output relations in all human languages. With partially-ordered constraints, two constraints allow 3 different languages. Any particular language has to select either A>B, B>C or A=B so the premise is not that there is only one universally possible grammar, rather, grammars are drawn from a universe populated by three possibilities. For 2 constraints; as you can imagine, if you expand the set of constraints to 10K or so, there are more possibilities.
"Implicational universal" is an old term of art (coming, non-ironically, from Stanford) originated by Greenberg, to the effect that "If a language does X, it must do Y". This is instantiated in older OT models via the concept of "harmonic bounding". This is a way of saying that not every descriptively imaginable situation can be realized, given some theory of what the primitives of OT are.