If upon examining the certificates of the boards of canvass it shall appear to the Governor that there has been a failure to choose 1 or more of the electors of a President and Vice President of the United States to be appointed in this State or, if from any cause such electors shall fail to be chosen, the Governor shall immediately issue writs for convening the General Assembly, at Dover, on the fourth Monday of the same November, and the elector or electors to be appointed in this State for the election of a President and Vice President of the United States and not chosen at the general election shall be appointed by ballot by the General Assembly so convened in joint meeting of the Senate and House of Representatives.