Council candidates shall qualify as provided by law and shall have the qualification and eligibility set forth herein. Each voter in the election may cast one vote for a candidate from his district, and one vote for a candidate for mayor. Any district councilman candidate receiving a majority of the total votes cast from the district in which he is a candidate shall be elected as a district councilman in his district. In the event that a district councilman candidate, should fail to receive such a majority, then another election shall be held upon the same day of the week three weeks thereafter to be called and held in the same mode and manner and under the same rules and regulations. In the second election there shall be two candidates for each place upon the council to be filled in such run-off election and these candidates shall be the two who received the highest number of votes. The candidate or candidates for the council receiving the highest number of votes cast in the second election shall be elected, so that in the first and second elections seven councilmen shall be elected. Regular municipal elections shall be held quadrennially thereafter under the same rules and regulations and in the same mode and manner as provided by law. The councilmen so elected shall take office upon the expiration of the terms of office of the present municipal officeholders. Each councilman shall hold office for four years, but shall serve until his successor shall have qualified. A councilman may succeed himself in office.