Within thirty (30) days after the date of issuance by the Secretary of State of a certificate of organization of a soil and water conservation district, nominating petitions may be filed with the State Soil and Water Conservation Committee to nominate candidates for commissioners of such district. The committee shall have authority to extend the time within which nominating petitions may be filed. No such nominating petition shall be accepted by the committee unless it shall be subscribed by twenty-five (25) or more owners of lands lying within the boundaries of such district. Landowners may sign more than one such nominating petition to nominate more than one candidate for commissioner but in no event shall a landowner sign more than three (3) such nominating petitions. The committee is hereby authorized to enact and implement rules to provide that not more than one commissioner shall be a resident of any one county or supervisors district, unless there is no person qualified and willing to serve in another county or supervisors district. The committee shall give due notice of an election to be held for the election of three (3) commissioners for the district. The names of all nominees, on behalf of whom such nominating petitions have been filed within the time herein designated, shall appear, arranged in alphabetical order of the surnames, upon ballots, with a square before each name and a direction to insert an X mark in the square before any three (3) names to indicate the voter’s preference. All owners of lands lying within the district shall be eligible to vote in such election. Only such landowners shall be eligible to vote. The three (3) candidates who receive a majority of the votes cast in such an election shall be elected commissioners for such district. In the event any candidate fails to receive a majority, then the candidates receiving the largest number of votes shall run off in an election to be held two (2) weeks thereafter. The committee shall pay all the expenses of such elections, shall supervise conduct thereof, shall prescribe regulations governing the conduct of such election and the determination of the eligibility of voters therein, and shall publish the results of same.