The officers provided for in section one of this article, shall be elected by the qualified electors of the State at the time and place of voting for members of the Legislature, and the persons respectively having the highest number of votes cast for the office voted for shall be elected; but if two or more shall have an equal and the highest number of votes for any one of said offices, the two houses of the Legislature, at its next regular session, shall elect forthwith by joint ballot one of such persons for said office.