Mind control ties are highly advanced mind control devices created by Ford Pines. One is worn by the person being mind-controlled, while the other is worn by the controller, with the wearer of the former being forced to mimic the words and movements of the controller.
Sometime before the events of the series, Ford made the ties for the "masters" of Ronald Reagan and kept the ties afterwards.
Later, during the election for the new mayor of Gravity Falls, Oregon, Ford gives the ties to Dipper after he tells him that Stan isn't doing well in the elections. To convince Stan to use the tie, the twins lie to him that it's his "lucky tie."
On the final day of the election, Stan decides to not wear the other mind control tie, and after Dipper gets angry and reveals the true nature of the ties, Stan bolts out of Greasy's Diner in anger.