If, after a reasonable period of negotiation over the terms of a collective bargaining agreement, a deadlock exists between a public employer and an organization, the labor relations agency may appoint a competent, impartial, disinterested person to act as mediator in any dispute either on its own initiative or on the request of one of the parties to the dispute. The parties may also select a mediator by agreement or mutual consent. It is the function of the mediator to bring the parties together voluntarily under such favorable auspices as will tend to effectuate settlement of the dispute, but neither the mediator nor the labor relations agency has any power of compulsion in mediation proceedings.