The third winding converts a current balun into a voltage balun. If the
antenna is completely symmetrical with respect to ground, the third
winding carries no current and does nothing. If the antenna isn't
symmetrical, the third winding forces an imbalance in current between
the antenna halves. The difference current flows on the transmission
line as a common mode current. So at best it does nothing, at worst it
causes the very problem a balun is intended to prevent.

There's more about this at http://eznec.com/Amateur/Articles/Baluns.pdf.

Roy Lewallen, W7EL