Two members of the county central committee for each political party shall, at the precinct caucuses, be elected from each precinct. The term of office of a member shall begin at the time specified by the party’s state constitution or bylaws and shall continue for two years and until a successor is elected and qualified, unless sooner removed by the county central committee for inattention to duty or incompetency. The party’s state constitution or bylaws may permit the election of additional central committee members from each precinct in a number proportionate to the vote cast for the party’s candidates for office in the respective precincts at preceding general elections.