Del. Code tit. 15 § 7332
In the joint meeting provided for by § 7331 of this title there shall be a distinct balloting for each elector, and a majority of all the votes given shall be necessary to an appointment; but if upon any ballotings 2 persons only shall be voted for and each shall receive an equal number of votes, the President of the Senate shall give an additional casting vote; if upon twice balloting in succession more than 2 persons be voted for and 1 of such persons on each balloting receive one half the number of all the votes given, the President of the Senate may, on the second balloting, give an additional casting vote to the person having one half of the number of all the votes given, or, if that person decline, the Speaker of the House of Representatives may, if the Speaker think proper, give an additional casting vote to the person having one half of such vote.
15 Del. C. § 7332