The supervisors of each district shall designate a chairman and may from time to time change their chairman. The term of office of each supervisor shall be 3 years, excepting that for those first appointed there shall be one for one year, 2 for 2 years, and 2 for 3 years. A supervisor may succeed himself in office, and he shall hold office until his successor has been appointed and has qualified. Vacancies shall be filled for an unexpired term, and removal from the district shall constitute a vacancy. Successors to fill an unexpired term or a full term shall be appointed by the state conservation committee. A majority of the supervisors shall constitute a quorum and the concurrence of a majority in any matter within their duties shall be required for its determination. A supervisor shall receive no compensation for his services, but he shall be entitled to expenses, including traveling expenses, necessarily incurred in the discharge of his duties.