From a set of choices and a weak order on that set you can partition the set
into equivalence classes:
define: X/~ == { {x} : x in X, forall y in {x} y~x }
This partitions the choice set into a set of disjoint subsets.
Union of subsets = X.
Furthermore, you can introduce a strict order on X/~.
This is because:
forall a in {x} and b in {y}: a > b <=> x>y