Every district under a minority representation plan shall be entitled to 3 alderpersons. Alderpersons shall hold their offices for 4 years and until their successors have been elected and qualified, except in cities that have adopted a 2 year term under Section 3.1-10-65. There shall be elected in each district as many alderpersons as the district is entitled to. In all of these elections for alderpersons, each elector may cast as many votes as there are alderpersons to be elected in the elector’s district, or may distribute his or her votes, or equal parts of the votes, among the candidates as the elector sees fit. The candidate highest in votes is elected if only one alderperson is elected; the candidates highest and next highest in votes are elected if only 2 alderpersons are elected; and the 3 highest candidates in votes are elected when 3 alderpersons are elected. Vacancies shall be filled as provided in Sections 3.1-10-50 and 3.1-10-55 by either interim election or appointment. An appointment to fill a vacancy shall be made within 60 days after the vacancy occurs. The requirement that an appointment be made within 60 days is an exclusive power and function of the State and is a denial and limitation under Article VII, Section 6, subsection (h) of the Illinois Constitution of the power of a home rule municipality to require that an appointment be made within a different period after the vacancy occurs.