In the event of the existence of any labor dispute which cannot be settled by negotiation between the charitable hospital employers and their employees, either such employers or employees may petition and avail themselves of the provisions of sections 179.01 to 179.17, insofar as sections are not inconsistent with the provisions of sections 179.35 to 179.39. If such dispute is not settled within ten days after submission to mediation, any unsettled issue concerning terms and conditions of employment, and other conditions of employment concerning union security shall, upon service of written notice by either party upon the other party and the commissioner, be submitted to the determination of a board of arbitrators whose determination shall be final and binding upon the parties. For public employers, "terms and conditions of employment" has the meaning given it in section 179A.03, subdivision 19. The board of arbitrators shall be selected and proceed in the following manner, unless otherwise agreed between the parties: the employers shall appoint one arbitrator, the employees shall appoint one arbitrator, and the two arbitrators so chosen shall appoint a third arbitrator who shall act as chair and who shall receive reasonable compensation for the work; but if said arbitrators are unable to agree upon the appointment of such third arbitrator within five days after submission to arbitration, the commissioner shall submit five names to the parties and the parties shall select the third arbitrator, who shall act as chair, from the five submitted by the commissioner. The selection of the third arbitrator shall be by the process of elimination, with the parties taking turns at striking names from the list of five submitted by the commissioner, until only one name remains. If the parties are unable to agree with respect to which party shall take the first turn for the purpose of striking a name, it shall be decided by the flip of a coin. Each party shall be responsible for compensating the arbitrator of their choice, and the parties shall share equally the compensation paid to the third arbitrator. The board of arbitrators shall serve as a temporary arbitration tribunal and shall have the powers provided for commissioners under section 179.08. The board of arbitrators shall make its determination with all due diligence and shall file a copy of its report with the commissioner.