Upon receipt of the base map the board of directors of the district shall appoint a board of three appraisers subject to the written approval of the county legislative authority of the county within which the major portion of the district is situated, whose duty it shall be to determine the ratio of benefits which the several tracts of land shall receive with respect to each other from the organization and operation of the district and the construction and maintenance of the district works in accordance with the comprehensive plan therefor adopted by the directors of the district.