WASHINGTON — On Dec. 19, 2016, a little more than a month after the presidential election, members of the Electoral College gathered around the nation to cast their votes. Ten of them went rogue.

A swing by that number of electors would have been enough to change the outcomes in five of the previous 58 presidential elections, according to a petition filed last week in the Supreme Court. In the 2000 election, after an assist from the Supreme Court, George W. Bush beat Al Gore by just five electoral votes.

The petition asked the justices to decide whether “faithless electors” were free to disregard pledges they made to vote for their own parties’ candidates. It urged the court to act quickly. “This case permits the court to issue a decision outside of the white-hot scrutiny of a contested presidential election,” the petition said.

Deciding the issue in the context of an actual election could do lasting damage to the Supreme Court, said Lawrence Lessig, a law professor at Harvard who filed the petition on behalf of three Democratic electors from Washington State who were fined $1,000 each for casting their electoral votes for Colin L. Powell rather than for Hillary Clinton.