The committee shall consist of a member from each of the following Senate committees: Banking and Commerce, Industrial Relations, Local Government, Public Employment and Retirement, and Revenue and Taxation and a member from each of the following Assembly committees: Finance, Insurance and Commerce, Labor and Employment, Local Government, Public Employees and Retirement, and Revenue and Taxation. The members shall be selected in the manner provided for in the Joint Rules of the Senate and Assembly. The committee shall elect its own chairman. Vacancies occurring in the membership of the committee between general sessions of the Legislature shall be filled in the manner provided for in the Joint Rules of the Senate and Assembly. A vacancy shall be deemed to exist as to any member of the committee whose term is expiring whenever such member is not reelected at the General Election.