[jcranmer]

The electoral college was originally intended to have the states appoint some grandees who would get together and discuss whom the best candidate for president would be (for an election system that actually works like this today, imagine the papal conclaves). This system worked like this approximately once, and failed catastrophically by the fourth election, which prompted the slight adjustment that we see today. Electors weren't regularly selected by popular vote until after that change, largely complete by the 1820s.

Meanwhile, the reason for the electoral allocation reflects one of the most fundamental compromises in the design of the federal system: is the national government be representative of the people, or is it representative of the states? The answer is it's both--that's why there's one house for the people and one house for the states (the Senate). And the number of electors for the president is similarly a compromise, giving one vote for each member of both houses. (Again, recall that senators were not elected by popular vote until the 20th century).

There was no concept of a rural/urban political divide, because urbanization really wasn't a thing in 1787. The overarching concern of the people who wrote the Constitution was balancing the powers of a state like Virginia versus Rhode Island--the small state/large state divide is the major focal point of discussion--although there was also a contentious issue over the role of slavery (of course, in 1787, most states were slave states--only Massachusetts had fully abolished slavery by that point, although the rest of New England had just adopted a gradual abolition program) which yields the ⅗ compromise.