Should a majority of the eligible members of a retirement system established by the state or by a political subdivision thereof, in a referendum held in accordance with section 218(d) (3) of the Federal Social Security Act, vote favorably for inclusion of positions covered by said retirement system under said Federal Social Security Act, the governor, on behalf of the state of Idaho, is hereby empowered to enter into an agreement with the secretary of health, education, and welfare of the United States for the purpose of covering said positions under said Federal Social Security Act. Such agreement may contain such provisions relating to coverage, benefits, contributions, effective date, modification and termination of agreement, administration, and other appropriate provisions as the governor and the secretary of health, education, and welfare shall agree upon, consistent with the provisions of the Federal Social Security Act.