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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 $b~R'~a$?

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    $\begingroup$ In math, $R'$ is usually referred to as the inverse relation of $R$. In economics, I have never seen such a definition, but I would say that "inverse" preferences make perfect sense. $\endgroup$ – Oliv Feb 5 '16 at 23:27
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@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 $R$.

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