The origins of the electoral college are a little more complicated than both of you are making it. Some of the framers/founders believed that democracy was essential, others believed it was something to be feared. Essentially, it boils down to a compromise within the Constitutional Convention. Instead of indirect elections in all cases, Madison believed that the people needed a direct stake in their government. This is why we ended up with direct elections to the House of Representatives. However, the Senate and the Presidency and the Judiciary, were implied to be higher offices that shouldn't be left to the people. Or in one founders opinion, "mobacracy."
One of the things that doesn't get talked about in the system of checks and balances is that indirect elections (the electoral college, appointments to the Supreme Court) are a direct attempt by the founders/framers to check the people. Or the will of the majority. In other words, many of our founders believed that the people, when conglomerated into large majorities with a single passion, could subvert the government and threaten the public good.
The reason we have two houses with different forms of representation is the result of another compromise. Our legislature is modeled on English Parliament. House of Lords and House of Commons. Senate and House of Representatives respectively. If Madison had his way, both houses would have been based on population. His idea of pure republican representative government. Because the smaller states feared that larger states would bully the smaller, the Senate is comprised of equal representation. The House, by population. Each house of Congress has different powers for different reasons.
If you ever have a lifetime to kill, read The Federalist and Madison's Notes on the Constitutional Convention. What's awesome is that they're finally online, so anyone who actually wants to know and understand our govt. can get them for free. Someone should tell Palin, Bachman, and Perry. They could stand to learn a thing or two.
But incantius is right, the proper form of our govt. is a Federal Democratic Republic. Federal because of our geographic State and National government distinction. Republic because of the representative form. And the Democratic element is more centered around our rights and liberties, though direct elections to the House would fit in with that distinction.