“Electors, once appointed, are free to vote as they choose,” Judge Carolyn B. McHugh wrote for the majority of a divided three-judge panel. “While the Constitution grants the states plenary power to appoint their electors, it does not provide the states the power to interfere once voting begins, to remove an elector, to direct the other electors to disregard the removed elector’s vote or to appoint a new elector to cast a replacement vote.”

In a petition seeking Supreme Court review in the case, Colorado Department of State v. Baca, No. 19-518, lawyers for Colorado wrote that “states may require electors to vote consistent with the state’s popular vote.” The appeals court’s decision, the petition said, threatens “to undermine the democratic principles underpinning over two centuries of electing United States presidents.”

The framers of the Constitution seemed to contemplate that electors would use independent judgment, the Supreme Court has said. “Doubtless it was supposed that the electors would exercise a reasonable independence and fair judgment in the selection of the chief executive,” Chief Justice Melville Fuller wrote in an 1892 Supreme Court decision. Over time, he added, “the original expectation may be said to have been frustrated.”

Alexander Hamilton described the original expectation in the Federalist Papers. “Men chosen by the people for the special purpose” of selecting the president, he wrote, “will be most likely to possess the information and discernment requisite to such complicated investigations.”

Judge McHugh of the 10th Circuit said the text of the Constitution also supports elector independence. The words of the relevant provisions, including “elector,” “vote” and “ballot,” she wrote, “have a common theme: They all imply the right to make a choice or voice an individual opinion.”

On election night in 2016, the electoral vote was expected to be 306 for Donald J. Trump and 232 for Mrs. Clinton. In the end, though, it was 304 to 227.

Seven electors succeeded in voting for other candidates. A fourth Democratic elector in Washington State voted for Faith Spotted Eagle, a Native American tribal leader and prominent opponent of the Keystone XL pipeline, and a Democratic elector in Hawaii voted for Senator Bernie Sanders of Vermont. Republican electors in Texas voted for Mr. Kasich and Ron Paul, a former representative of Texas.