Title 9, Chapter 9, Section 68
If an arbitrator selected by one of the parties should cease to serve for any reason, the party who chose the arbitrator shall then choose another in his place. If the arbitrator chosen by the other arbitrators shall cease to serve for any reason, the arbitrators chosen by the parties shall choose another in his place. If the arbitrators chosen by the parties are unable to agree upon the third arbitrator, the third arbitrator shall be appointed as provided in subsection (b) of Code Section 9-9-67. An arbitrator chosen pursuant to this Code section shall have all the powers of the original arbitrator.