The Mayor shall preside at all meetings of the Council but shall have no vote therein, except in the event of a three-to-three tie in the vote of Council, in which case the Mayor shall be entitled to vote to break the tie. In the event the Mayor votes for passage of a measure, said measure shall then be considered to have received the favorable vote of four (4) of the six (6) councilmen. The Mayor may, however, introduce ordinances and resolutions, and take part in the discussion on all matters coming before the Council.