The Joint Committee on Government and Finance, heretofore existing under a joint rule of the Senate and House of Delegates, is hereby continued as a statutory body. This committee shall be composed of seven members of the Senate, six of whom shall be appointed by the President of the Senate, and seven members of the House of Delegates, six of whom shall be appointed by the Speaker of the House of Delegates. The six members appointed by the President of the Senate shall include the majority leader of the Senate, the minority leader of the Senate, the chairman of the Senate committee on the judiciary and the chairman of the Senate committee on finance. The six members appointed by the Speaker of the House of Delegates shall include the majority leader of the House of Delegates, the minority leader of the House of Delegates, the chairman of the house committee on the judiciary and the chairman of the house committee on finance. The President of the Senate and the Speaker of the House of Delegates shall be members of the committee and cochairmen thereof. Not more than five members of the committee from each house shall be members of the same political party: Provided, That in the event the membership of a political party is less than fifteen percent in the House of Delegates or Senate, then the membership of that political party from the legislative house with less than fifteen percent membership may be one from that house. The members shall serve until their successors shall have been appointed as heretofore provided.