After a public hearing, the Commission shall appoint an experienced neutral third party to serve as labor relations administrator for 1 year. After the term for the labor relations administrator appointed under subsection (a) of this section expires, the exclusive representative or representatives and the Commission shall jointly appoint a labor relations administrator from a list of five nominees on whom they have agreed. If the exclusive representative or representatives and the Commission are unable to jointly agree on a list of five nominees or are unable to jointly appoint a labor relations administrator from the list, the Commission shall request from the American Arbitration Association a list of 15 candidates located in the State or the Washington, D.C. metropolitan area. The Commission and the exclusive representative or representatives shall select the labor relations administrator by each of the parties striking one name from the list until the last name remains. A random drawing shall determine the order in which the parties shall strike names. The labor relations administrator shall be appointed for a term of 3 years. After the term for the labor relations administrator appointed under subsection (a) of this section expires and after a public hearing on the appointment, if no exclusive representative has been certified under this subtitle, the Commission shall appoint the next labor relations administrator for a term not exceeding 1 year. A labor relations administrator is eligible for reappointment.