Article 2, Section 1, Paragraph 3
The Electors shall meet in their respective States, and vote by Ballot for two Persons, of whom one at least shall not be an Inhabitant of the same State with themselves. And they shall make a List of all the Persons voted for, and of the Number of Votes for each; which List they shall sign and certify, and transmit sealed to the Seat of the Government of the United States, directed to the President of the Senate. The President of the Senate shall, in the Presence of the Senate and House of Representatives, open all the Certificates, and the Votes shall then be counted. The Person having the greatest Number of Votes shall be the President, if such Number be a Majority of the whole Number of Electors appointed; and if there be more than one who have such Majority, and have an equal Number of Votes, then the House of Representatives shall immediately chuse by Ballot one of them for President; and if no Person have a Majority, then from the five highest on the List the said House shall in like Manner chuse the President. But in chusing the President, the Votes shall be taken by States, the Representation from each State having one Vote; A quorum for this purpose shall consist of a Member or Members from two thirds of the States, and a Majority of all the States shall be necessary to a Choice. In every Case, after the Choice of the President, the Person having the greatest Number of Votes of the Electors shall be the Vice President. But if there should remain two or more who have equal Votes, the Senate shall chuse from them by Ballot the Vice President.*
Breaking the Tie
There are rare instances where there may be a tie for office, after the electoral votes are counted. In this situation, the House would vote to break the tie. This was to be done at the time of the count so the election process would have an outcome.
In the case where there is no majority, or any clear winner of the electoral process, then the House would place the five highest vote getters on a ballot for election. This would be the only means by which citizens would have a say in the choosing of a president, and this is through their representative in the government.
The Apostles when seeking to replace Judas resolved a tie. They had narrowed the field down to two, and used the Biblical method of the final choice by casting lots.
Acts 1:23-26, "And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias. And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen, That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place. And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles."
This method is superior because a basis of qualification is laid out first, and candidates presented are narrowed down based on qualification. Finally, from the candidates, lots are cast to determine the one to serve.
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