In the performance of the duties of conciliation, mediation or arbitration, the board shall be represented by a panel of three of its members, except that, in arbitration, a single public member of the board may arbitrate instead of a panel by joint agreement of the parties involved, and in such event such member shall have all the powers of a panel. In each case, the employee or his representative appearing before said board shall be permitted to designate the labor member of the Board of Mediation and Arbitration who shall serve and the employer or his representative appearing before said board may designate the employer member of the Board of Mediation and Arbitration who shall serve. The chairman of the Board of Mediation and Arbitration shall serve as the member representing the public; if he is unable to serve, the deputy chairman shall serve in his stead. Whenever members are unable to serve, alternate members may be delegated to serve in accordance with the provisions of this chapter.