N.M. Stat. § 44-7A-12
Appointment of arbitrator; service as a neutral arbitrator.
(a) 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 appointed pursuant
to 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.