WASHINGTON — On Tuesday, call him the tiebreaker.

A vice president does not have much on his plate, as far as constitutional responsibilities go. He presides over the official count of electoral votes once, possibly twice, and, in the meantime, he waits in the wings in case the president becomes incapacitated.

But Vice President Mike Pence is expected to demonstrate the position’s unique duty, and in historic fashion: In his capacity as president of the Senate, he is expected to cast the deciding vote to confirm Betsy DeVos as President Trump’s education secretary — the first time a vice president has had to resolve a tie on a cabinet nomination in the nation’s history.

Allowed to vote only when the Senate is deadlocked, vice presidents have a long history of settling disputes. John Adams, for instance, cast votes that helped determine the location of the United States capital and averted war with Britain.

Ahead of Mr. Pence’s potential vote, here is a look back at a few crucial moments in modern vice-presidential tiebreaking.