Under a partial ordering, a median may not be unique. Even under a total ordering this is true if some subset of elements form an equivalence class. But under partial ordering, the non-uniqueness can get much weirder.
I'm sure with more thought, weirder things can be thought of. But just as a quick example, it would be easy to write classes such that:
a < b < c < a
In such a case (or expand for an odd number of distinct things), it would be reasonable to call ANY element of [a, b, c] a median. That's funny, but it is not imprecise.
--
Keeping medicines from the bloodstreams of the sick; food
from the bellies of the hungry; books from the hands of the
uneducated; technology from the underdeveloped; and putting
advocates of freedom in prisons. Intellectual property is
to the 21st century what the slave trade was to the 16th.