To mediate between two (or more) parties in conflict. We need someone to arbitrate between these two departments before their in-fighting affects the whole company. As a marriage counselor, I specialize in arbitrating between couples who are having difficulty communicating.
arbitrate between (someone and someone else)
to mediate between two disagreeing parties; to help two disagreeing parties to resolve their differences. Jane was called upon to arbitrate between the workers and the manager. I arbitrated between Fred and his ex-wife.