The county council shall annually elect one of its members as chair and one as vice-chair who shall act in the absence of the chair. The council shall be responsible for its own organization, the rules of conduct of its business and for the employment and supervision of such persons as it deems necessary to assist it in the performance of its duties. A majority of the council shall constitute a quorum at all meetings. Council action shall require at least a majority of the entire council except as provided by this charter or ordinance.