BANGOR — U.S. Rep. Bruce Poliquin asked a federal judge late Tuesday to order a new election in Maine’s 2nd Congressional District if the judge won’t declare Poliquin the winner.

The two-term Republican claimed victory based on the first round of ranked-choice voting results in the midterm election earlier this month.

Poliquin’s attorneys filed paperwork with the U.S. District Court in Bangor claiming ranked-choice voting is unconstitutional and that allowing Democrat Jared Golden of Lewiston to be declared the winner would be unfair.

Golden emerged as the victor after ranked-choice votes were counted by state officials. He captured more than 3,500 votes beyond Poliquin’s tally once the second and third choices of voters who initially backed one of the two independent candidates in the race were added to the totals.

District Court Judge Lance Walker, recently appointed by President Donald Trump, has not shown much sympathy for Poliquin’s argument that ranked-choice voting is unconstitutional. His initial ruling on a Poliquin request to stop the ranked-choice tally allowed the count to continue, and Walker pointed out that Maine voters had chosen to use the ranked-choice system.

Poliquin’s lawyers, though, are pressing forward in the hope that Walker may see their arguments in a different light once all of their briefs are filed and he’s had time to research it more. They may also have their eye on possible appeals if Walker remains skeptical.

Lee Goodman, Poliquin’s chief counsel, said in his brief that the right to vote “is being undermined” by Maine’s new method that replaced “the plurality-based, single-election system used in this state for nearly 140 years with an exotic, ranked-choice voting system described as ‘costly,’ ‘confusing’ and ‘depriving voters of genuinely informed choice.’”

Poliquin’s case boils down to the proposition that in ranked-choice voting, those casting ballots cannot know the identities of the candidates who will remain in contention after the first round, forcing them “to guess whether there would be an ‘instant runoff’ election and who the candidates would be.”

That “lack of access to such basic information” prevents them, Goodman argued, “from choosing among candidates and casting their votes effectively,” a situation he insisted violated both the 1st and 14th amendments to the U.S. Constitution.

“This system forces voters to make blind guesses about the ultimate matchup in the final round of vote,” said James Gimpel, a University of Maryland political science professor who offered his testimony to the court Wednesday to bolster Poliquin’s case.

Gimpel testified that in his study of the results, he found that 46 percent of voters only made one first-place pick and no others.

Another 10 percent marked a first- and second-place selection but stopped there. Only 3 percent of voters ranked a candidate in all five of the possible positions — the four candidates plus a write-in slot.

Perhaps surprisingly, four out of five of those who filled in each possible round picked the same person in every round — 5,233 of them opting for Poliquin in rounds one through five.

“One can interpret these completion patterns in various ways,” Gimpel said, “but certainly the very small percentage filling in the ballot at all five ranks suggests no small amount of misunderstanding about the way the system is supposed to work.”

“That so many chose not to rank alternative candidates, but expressed a preference for the same candidate across all ranks also evidences some combination of misunderstanding and/or disregard for the theory motivating the instant runoff,” he said.  

Since there is no clear remedy to resolve the problem, Goodman said, Walker ought to declare the first-round winner the victor — an idea Walker pretty much dismissed at a hearing this month — or require a new election that does not rely on ranked-choice options.

Lawyers for the state and Golden countered the legal arguments made by Poliquin in a court hearing two weeks ago. They said voters — and the candidates — knew the rules and that the election went smoothly.

Federal courts have generally been wary of intruding into elections that have already been held. But in “exceptional” occasions they have ordered new ones.

On Monday, Poliquin asked the Maine Secretary of State’s Office for a hand recount of votes in the race, which pitted him against Golden and independents Tiffany Bond of Portland and Will Hoar of Southwest Harbor.

If a new election is ordered, it is not clear whether the same candidates would necessarily appear on the ballot.

“I’m going to see this to the end,” Poliquin told Portland’s WGAN radio Wednesday.

Walker may make a decision before Dec. 14, when Gov. Paul LePage is supposed to certify the results and send them to the U.S. House of Representatives.

The U.S. Constitution says the House “shall be the Judge of the Elections, Returns and Qualifications of its own Members.”

The Democrats, who take control of the House on Jan. 3, are unlikely to accept Poliquin’s arguments given Secretary of State Matt Dunlap has already declared Golden the victor.

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U.S. Rep. Bruce Poliquin, R-Maine, leaves the Longworth House Office Building on Capitol Hill in Washington on Wednesday. Poliquin, who lost to Democratic challenger Jared Golden of Lewiston, is in an ongoing legal battle to challenge the results of the election. (AP Photo/J. Scott Applewhite)