(a) The supervisors shall designate a chairman and from time to time may change such designation.

(b) The term of office of each elected supervisor shall be four years. An elected supervisor shall hold office until his successor has been elected and has qualified.

(c) Vacancies shall be filled for the unexpired term. The selection of successors to fill an unexpired term or a full term shall be made in the same manner in which the retiring supervisors were selected.

(d) A majority of the supervisors shall constitute a quorum; and the concurrence of a majority of the supervisors in any matter within their duties shall be required for its determination.

(e) The commission is authorized to fix a per diem payment for supervisors; in addition thereto, such supervisors shall be entitled to the regular mileage allowances provided for state employees if such supervisors travel by private conveyance and to their actual travel expenses if they travel by public conveyance.