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This might be related to : Symmetric and asymmetric preferences.
In your experience, what is the best terminology to denote a pair of preference relations $(R,R')$ over some set of alternatives $A$ such that, for all $a,b \in A$, $a~R~b$ implies $b~R'~a$?
@Oliv's comment lead me to the following wikipedia article https://en.wikipedia.org/wiki/Inverse_relation which indicates that the term "inverse" is used to define the kind of relation between $R$ and $R'$ that I described in the question.
The wikipedia article recommends to use $R^{-1}$ to denote the inverse relation of $R$.
