In the 1960 presidential election, an additional one vote per precinct in Illinois, Missouri, New Jersey, and Texas may have altered the course of America's modern history by denying John F. Kennedy the presidency and placing Richard Nixon in the White House eight years earlier.
In 1962, the governors of Maine, Rhode Island, and North Dakota were all elected by a margin of one vote per precinct.
In 1984, a Monroe County, Florida commissioner was elected by one vote.
In 1994, the U.S. House of Representatives enacted a law banning specific classes of assault weapons. The vote was initially tied but one member changed his vote to approve the ban.
In 1995, bills proposing amendment to the U. S. Constitution required a 2/3 vote of each House in order to be approved. When the balanced budget amendment bill came before the U.S. Senate, the measure failed by one vote. Mark Hatfield, Republican from Oregon, was the sole Republican failing to vote with other members of the Republican Party, which was then the majority party of the U.S. Senate. When it became apparent the measure would fail, Senate Majority Leader Bob Dole changed his vote to enable him to bring the matter back up under parliamentary rules for a vote in the future.