> IRV can be implemented as either requiring complete ordering or allow partial ordering (you have n candidates, you can assign each one level 1..n, but you may use the same level for more candidates to describe partial ordering).

Technically, that’s a complete ordering with unforced preferences, not a partial ordering.

A ballot with a partial ordering would be won for which for some pair of candidates A, B, none of A> B, A<B, nor A=B would be true. Equal preference and absence of preference are different.

A ballot that worked this way would be a meaningful extension in existing ranked preference methods that aggregate pairwise preferences from individual ballots, lile ranked pairs. (Whether the effect would be desirable is not something I’ve really analyzed, but that kind of method would naturally make distinct use of the information.)