Find out how to get an arbitrator appointed and the appointment process. Asp for case information.Arbitration should also be considered as a way of avoiding publicity and exposure that can come with a public jury trial. The case shall then proceed to arbitration as provided in Rules 72 to 76, Arizona Rules of Civil Procedure. d. Appointment of Arbitrators. A person that brings a lawsuit in Arizona is required to fill out a form stating the type and estimated value of damages they seek. Among those who disagreed, most thought the time period was too short. Arbitration as an ADR Family Law Process.