Upon the request of any interested party to an actual or potential labor dispute, the director shall have the power to mediate the dispute. The director or any interested party may apply to the governor for appointment of a mediator or a mediation panel of not less than three (3) citizens who are objective in matters involving labor disputes, and the governor shall, if the public interest will be served thereby, appoint such a mediator or mediation panel. Such mediator or mediation panel shall be paid actual expenses by the interested parties while engaged in such public business. Neither the director, the governor, nor any mediator or member of any mediation panel shall be authorized to arbitrate any labor dispute.