If the proposal is approved by a majority of the votes cast thereon, the board of supervisors shall file a certificate, signed by the chairman of the board and duly dated, with the Secretary of State, reciting that the proposal to adopt subdivision (d) of Section 16 of Article VI of the California Constitution as applicable to the judge of the superior court of the county was approved by a majority of the votes cast thereon at the election. Upon the filing of the certificate the provisions of subdivision (d) of Section 16 of the California Constitution shall thereupon be applicable to the judge of the superior court of that county, and effective as to all vacancies in the office occurring after the date of filing of the certificate.