If the majority of the four members of the board appointed pursuant to subdivisions (a) and (b) of Section 101103 fail to appoint the fifth member of the board within 30 days after the appointment of such four members, then the fifth member shall be appointed within 30 days thereafter by the majority vote of a conference committee composed of five members selected as follows: two members of the board of supervisors chosen by that board, two members of the City Council of the City of Bakersfield chosen by the council, and one member chosen by the majority of the four other members so appointed.