Mich. Comp. Laws § 691.1691

Sec. 11. (1) If the parties to an agreement to arbitrate agree on a method for appointing an arbitrator, that method must be followed, unless the method fails. If the parties have not agreed on a method, the agreed method fails, or an arbitrator appointed fails or is unable to act and a successor has not been appointed, the court, on motion of a party to the arbitration proceeding, shall appoint the arbitrator. An arbitrator so appointed has all the powers of an arbitrator designated in the agreement to arbitrate or an arbitrator appointed by the agreed method. (2) An individual who has a known, direct, and material interest in the outcome of the arbitration proceeding or a known, existing, and substantial relationship with a party shall not serve as an arbitrator required by an agreement to be neutral.