Article I, Section 3 of the Constitution specifies that The Vice President is the President of the Senate. The Vice President has no vote unless to break a tie in some matter before the Senate.
Therefore, if the election leads to a 50-50 party split in the Senate, the Vice-President's vote will give the majority to his or her party.
Currently, the U.S Senate is controlled by the Republicans. They have 54 Senate seats, Democrats 44, with 2 independents caucusing as Democrats (effectively giving them 46 seats). In 2016, 34 Senate seats are up for election, 10 held by Democrats, 24 by Republicans. Since Democratic Vice-President Joe Biden will break any ties, Democrats must gain at least 4 seats, for a minimum of 50 total, to take control in early January, 2017.
However, since 2016 is also a presidential election year, there will be a new vice-president as of January 20, 2017. If the Republicans win the presidency in 2016 and the Senate is tied, Democratic control will be short-lived, as the new Republican vice-president will break any ties once he or she is inaugurated.
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