When an uninvolved, impartial person is called in to help settle a dispute, it's called arbitration. The person in charge of the arbitration acts like an official referee, helping both sides come to an agreement.
The noun arbitration comes to English via the Latin word arbitrari, meaning "to judge." In English, arbitration is both the process of using an arbiter to settle a dispute and the act of that arbiter making a judgment. Many parents know that if the arbitration of your kids' argument was deemed unfair by both kids, you've usually made the right decision.