Federalist 68 outlined
Hamilton’s understanding of the Electoral College
Federalist No. 68 is the continuation of Hamilton’s analysis of the presidency, in this case concerned with the mode of selecting the United States President. Here, Hamilton argues for our modern conception of the Electoral College, though in the case of an Electoral tie, the power would be given to the House of Representatives to vote on the election of the president.
In justifying the use of the Electoral College, Hamilton focuses on a few arguments dealing with the use of the Electoral College instead of direct election. First, in explaining the role of the general populace in the election of the president, Hamilton argues that the, “sense of the people”, through the election of the electors to the Electoral College, should be a part of the process. The final say, however, lies with the electors, who Hamilton notes are,
Men most capable of analyzing the qualities adapted to the station and acting under circumstances favorable to deliberation, and to a judicious combination of all the reasons and inducements which were proper to govern their choice.
Therefore, the direct election of the president is left up to those who have been selected by the voters to become the electors. This indirect election is justified by Hamilton because while a republic is still served, the system allows for only a certain type of person to be elected president, preventing individuals who are unfit for a variety of reasons to be in the position of chief executive of the country.
This is reflected in his later fears about the types of people who could potentially become president. He worries that corrupted individuals could, particularly those who are either more directly associated with a foreign state, or individuals who do not have the capacity to run the country. The former is covered by Article II, Section 1, v of the United States Constitution, while the latter is covered by Hamilton in Federalist 68, where he notes that the person who will become president will have to be a person who possesses the faculties necessary to be a president, stating that,
Talents for low intrigue, and the little arts of popularity, may alone suffice to elevate a man to the first honors in a single State; but it will require other talents, and a different kind of merit, to establish him in the esteem and confidence of the whole Union, or of so considerable a portion of it as would be necessary to make him a successful candidate for the distinguished office of President of the United States
Hamilton, while discussing the safeguards, is not concerned with the possibility of an unfit individual becoming president, instead he says,
It will not be too strong to say, that there will be a constant probability of seeing the station filled by characters pre-eminent for ability and virtue.
This is copied from Wikapedia.