The Vice President's Job: The only duty the U.S. Constitution assigns the Vice President is to act as presiding officer of the Senate. But the Vice President also serves as ceremonial assistant to the President and is an important part of the President's administration.
The ancient Athenians used a democracy, while the U.S uses a democratic republic. So in other words we got some of the democratic part from the Athenians. Hope this helps. :)