The last remaining Republican congressman in New England filed an appeal Tuesday that seeks to undo the election of his Democratic opponent under Maine's new voting system, asking the court to act quickly as the swearing-in of new U.S. House members nears.

A federal judge last week rejected U.S. Rep. Bruce Poliquin's concerns over the constitutionality of ranked voting, a system used in November for the first time in a congressional race.

Poliquin lost his re-election bid to Democrat Jared Golden. His appeal asks the 1st U.S. Circuit Court of Appeals in Boston to reconsider his request to nullify the election's outcome and either declare him the winner or order another election.

Poliquin claims he should be the winner because he had the most first-place votes on Election Day. But Golden won the race in an extra round of voting in which two trailing independents were eliminated and their votes were reallocated.

In his appeal, Poliquin claims that ranked-choice voting "violated all voters'" constitutional rights. Poliquin says the judge's rejection of his requests "sidestepped the explicit questions presented, often casting the questions at a more superficial level of analysis."

Meanwhile, Golden's chief of staff, Aisha Woodward, said the judge's decision was "crystal clear" and called it the "best response" to Poliquin's appeal.

Poliquin's appeal comes just weeks before Golden is set to be sworn in Jan. 3.

But Congress doesn't have to wait for the litigation to wrap up before deciding whether to swear Golden in, said Edward Foley, constitutional law professor at Ohio State University's law school. That decision is in the hands of the newly Democratic controlled House, where House Democratic leader Nancy Pelosi earlier this month chided Republicans' fight against ranked-choice voting and Golden's win.

"Congress doesn't have to be controlled by the litigation in terms of deciding whether to seat the elected member," Foley said. "That's a decision Congress ultimately makes itself."

Another fight over a House race has been brewing in North Carolina , where Republicans want their candidate to take his seat in Congress in a still-undecided race marred by ballot fraud allegations.

But the fight there differs from Poliquin's lawsuit, which is about concerns over the system Maine used to tabulate winners.

Under ranked-choice voting, a system Maine voters approved in 2016, all candidates are ranked on the ballot, and a candidate who collects a majority of first-place votes is the winner. If there's no majority winner, then the last-place candidates are eliminated, and their second-choice votes are reassigned to the remaining field. The process is sometimes referred to as an instant runoff.

Poliquin has lambasted ranked-choice voting as being so "confusing" that it effectively disenfranchises voters.

Last week, U.S. District Judge Lance Walker said that critics can question the wisdom of ranked-choice voting, but that such criticism "falls short of constitutional impropriety." The judge rejected several of Poliquin's constitutional concerns and said the Constitution gives states leeway in deciding how to elect federal representatives.

Poliquin has also abandoned his request for a recount of Maine's election. The secretary of state's office said he is responsible for the "actual cost" of recount efforts.

Maine's top state court last year warned that ranked voting conflicts with the state's constitution, which says the winners of state-level races are whomever gets the most votes, or a "plurality." And so Maine uses ranked voting only in federal elections and state primary races, but not for general elections for governor or the Legislature.

Democratic Gov.-elect Janet Mills has vowed to seek to amend the state constitution so the system can be used in all elections.