Independence, by contrast, is an objective notion and is capable in many cases of being established or challenged at the appointment stage.
Lack of independence is a pointer towards potential partiality.
It is possible (if unlikely) that an arbitrator may not be entirely independent of both parties as a result of a relationship with one or the other or a connected third party, but may be able to set aside that relationship and come to a decision entirely impartially, based on the facts and the relevant law alone.