Rep. Bruce Poliquin and three of his constituents in Maine’s 2nd District are appealing a U.S. district court’s decision to uphold the constitutionality of the state’s new ranked-choice voting system that boosted Democrat Jared Golden over Poliquin, who had more first-place votes.

Poliquin’s lawyers will file a brief with the 1st U.S. Circuit Court of Appeals in Boston on Tuesday, the Portland Press Herald reported.

U.S. District Judge Lance Walker tossed out Poliquin’s arguments against Maine’s Ranked-Choice Voting Act, employed for the first time for federal elections this year, in a 30-page opinion issued last week.

“There is nothing inherently improper about an election that requires a contestant to achieve victory by a majority,” Walker wrote, adding that the Constitution leaves it up to the states to decide how best to administer democratic elections.

“Maine’s RCV Act reflects the view of a majority of the voting public in Maine that their interests may be better represented by the candidate who achieves the greatest support among those who cast votes, than by the candidate who is first ‘past the post’ in a plurality election dominated by two major parties,” Walker wrote.

Poliquin led Golden by less than a point on the first count, but since neither candidate received 50 percent of the vote, the state’s ranked-choice system kicked in to determine the winner. Among voters who did not rank Golden or Poliquin as their first choice, the former was ranked ahead of the latter on more ballots. In a head-to-head race using the ranked-choice system, Golden defeated the GOP incumbent by 3,500 votes.

Poliquin challenged the federal constitutionality of the ranked-choice system in a statement Monday evening.

“Every Mainer deserves to know if his or her vote cast for a candidate in federal office … under the complicated and confusing rank vote process will be fully legal moving forward,” Poliquin said. He noted that the Maine Supreme Court has already ruled the system illegal for selecting the state’s governor and state legislators.

Maine’s constitution has a clause making clear that candidates for office can win with a plurality of votes cast in their favor. The Constitution has no such clause in its guidance for state-administered elections.