§ 09-43-380

(a) If the parties to an agreement to arbitrate agree on a method for appointing an arbitrator, that method shall 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 application of a party to the arbitration proceeding, shall appoint the arbitrator. An arbitrator appointed by the court has all the powers of an arbitrator designated in the agreement to arbitrate or appointed under the agreed method. (b) 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 may not serve as an arbitrator required by an agreement to be neutral.