N.M. Stat. § 73-20-40
Within a reasonable time after each district election and after newly elected supervisors have completed the oath of office, the supervisors of a district shall organize and shall designate a chairman who shall be a supervisor and who shall serve at the pleasure of the supervisors. In the performance of district functions, a majority of supervisors shall constitute a quorum; the concurrence of the quorum majority shall be required to carry or to determine any matter of district business. Supervisors shall not receive compensation for their services but shall be entitled to be reimbursed in accordance with the provisions of the Per Diem and Mileage Act [10-8-1 to 10-8-8 NMSA 1978]. Supervisors may purchase group health insurance benefits for themselves and their dependents pursuant to the Group Benefits Act [Chapter 10, Article 7B NMSA 1978] and pursuant to the rules and procedures set forth by that act and the risk management division of the general services department.
NMS § 73-20-40