The committee shall consist of five members of the senate and five members of the house who shall be selected in the manner provided for in the rules of the senate and the rules of the house. The president of the senate and the speaker of the house shall select the members of the committee, including members of the majority leadership, members of the minority leadership, the chairperson of the senate ways and means committee, and the chairperson of the house finance committee. The chairperson of the senate ways and means committee and the chairperson of the house finance committee shall serve as co-chairpersons of the committee. Vacancies occurring in the membership of the committee shall be filled in the manner provided for in the rules of the senate and the rules of the house. A vacancy shall be deemed to exist as to any member of the committee whose term is expiring whenever the member is not reelected at the general election.