The electors shall designate their selections for governor and lieutenant governor as if these two offices were one and the same. The names of nominees for the governor and the lieutenant governor shall be grouped together in a set on the ballot according to which nominee for governor is seeking office with which nominee for lieutenant governor, as prescribed by law. An elector shall cast only one vote for both a nominee for governor and a nominee for lieutenant governor. The returns of every election for governor and lieutenant governor shall be sealed and transmitted to the seat of government of the state, and directed to the speaker of the house of representatives who shall open and publish them in the presence of both houses of the general assembly.