After the adoption and filing of a plat as required in Section 3-7-5 N.M. Stat. Ann., a board of arbitration shall be created which shall have seven members. Three of the members shall be selected as provided in Section 3-7-7 N.M. Stat. Ann.; three of the members shall be selected as provided in Section 3-7-8 N.M. Stat. Ann.; and one member shall be selected as provided in Section 3-7-9 N.M. Stat. Ann..