A candidate in said election receiving a majority of the votes cast for the position of mayor and for the position of councilman for the district for which he is a candidate, as the case may be, shall be declared elected. If none of the candidates for such position receives a majority vote, then none of the candidates for that office shall be elected and a run-off election shall be held among the two (2) candidates who receive the greatest number of votes for such position. In the event of a run-off, the City Council shall immediately order a run-off election, which shall be held not less than twenty (20) nor more than thirty (30) days after the canvass of the election in which a run-off is required. Notice of such run-off election shall be given and the election shall be held in the same manner as the general or special election in which the run-off occurred. At such election, only the names of the two (2) candidates who received the greatest number of votes for such position shall be printed on the ballot and any write-in votes cast for any other person shall be void and shall not be counted for any purpose.