Wyo. Stat. § 41-7-318
No person shall be declared elected as a commissioner who shall not be a landowner in said commissioner district and who shall not have received a majority of all votes cast by the qualified voters of said commissioner district. No election shall be invalid by reason of the fact that a majority of the acreage within the district was not represented at such election. Whenever the office of any elected commissioner shall become vacant by reason of death, resignation or other cause, the vacancy shall be filled by the surviving commissioners for the unexpired term. In case such vacancy is not so filled within thirty (30) days, the court shall fill such vacancy. All elected commissioners shall have the same qualifications and duties as herein prescribed for appointed or elected commissioners.
W.S. 41-7-318