In Art. II, Sec. 1 of the US Constitution, what is the reasoning for the requirement that the Electors vote for two persons, "of whom one at least shall not be an Inhabitant of the same State with themselves."
There was concern during the drafting of the Constitution that many people would know only or primarily their local officials and political figures, and thus that many electors would vote only for people from their own state, leading to many candidates, none of whom would have anything close to a majority. The provision referred to was intended to avoid this, and encourage a more national election. In practice the problem has not happened. This is arguably one of the consequences of the prompt rise of national political parties, which was not foreseen by the authors of The Federalist Papers nor by many (if any) of those who wrote about the Constitution during the ratification debates.
The Federalist #68 deals with the election of the President. It does not specifically mention this provision, but does say, while discussing the Electoral College:
The process of election affords a moral certainty, that the office of President will never fall to the lot of any man who is not in an eminent degree endowed with the requisite qualifications. 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.
The better choice and judgment of a national vs a mere state-wide electorate is a consistent theme though much of The Federalist, particularly the parts written by Madison.