The Constitution for the United States of America

Article 1
Section 3 - Paragraph 4

The Vice-President of the United States shall be President of the Senate, but shall have no vote, unless they be equally divided.

Because there are two Senators appointed by each State there will always be an even number of Senators permitted to vote. This raises the distinct possibility of tie votes and a provision had to be made to solve this problem. By making the Vice President the President of the Senate and letting him, or her, cast the deciding vote the problem was solved.

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