Rep. Bruce Poliquin is appealing a recent federal judge’s rejection of his lawsuit challenging the constitutionality of ranked-choice voting.

Poliquin and three other residents of Maine’s 2nd Congressional District filed a notice of appeal on Monday, four days after a U.S. District Court judge dismissed his constitutional argumentsand refused to order a new election. The case will go before the 1st U.S. Circuit Court of Appeals in Boston.

Poliquin, a two-term Republican, lost the 2nd District election to Democratic Representative-elect Jared Golden following the nation’s first use of ranked-choice voting to decide a congressional race. Poliquin trails Golden by more than 3,500 votes and has sought to overturn an election process that his campaign claims was confusing for many voters and potentially violated the U.S. Constitution.

U.S. District Court Judge Lance Walker rejected those arguments in a strongly worded, 30-page opinion. Walker ruled that nothing in the U.S. Constitution requires members of Congress be elected by “a plurality” of votes – rather than the majority required under ranked-choice voting.