Representative Bruce Poliquin of Maine, the only Republican House member from New England, said Monday that he was dropping his challenge to the state’s ranked-choice voting law, conceding that he lost his seat to his Democratic opponent, Jared Golden.

His decision means that Mr. Poliquin, a two-term incumbent, was the first choice of the most voters on Election Day in Maine’s heavily rural Second Congressional District but loses his race in the first federal general election decided by ranked-choice voting.

Under the system, voters can rank the candidates instead of just picking one. If no candidate gets a majority of the first-choice votes, the candidate who came in last is eliminated and those votes are redistributed to voters’ second-choice candidates. The process keeps going until someone has a majority.

In Mr. Poliquin’s race, there were two independent candidates, in addition to Mr. Poliquin and Mr. Golden. Although Mr. Poliquin led on Election Day, he did not receive a majority. When the two independent candidates were eliminated and their votes redistributed, Mr. Golden won by roughly 3,500 votes out of more than 280,000 originally cast.