Jared Golden, a Marine Corps veteran and Democratic state lawmaker in Maine, defeated New England’s lone House Republican, Bruce Poliquin, on Thursday, just two days after Mr. Poliquin filed a lawsuit to stop the counting of votes under the state’s new ranked-choice voting system.

Mr. Poliquin’s defeat in Maine’s Second Congressional District added to a swell of bad news for northeastern Republicans, who suffered heavy losses on Election Day, and gave Democrats another Republican seat in their takeover of the House.

And it added an intriguing new angle to the nation’s ferment over voting rules and options when Mr. Poliquin, the candidate who was the first choice of more voters, lost the race to Mr. Golden, who won on the basis of being the second or third choice of voters who initially chose two independent candidates who together got 8 percent of the vote.

A spokeswoman for the Maine secretary of state’s office said the results remained unofficial pending certification by Nov. 26. But, if certified, the results would make Mr. Golden the winner of a four-candidate race in which Mr. Poliquin received 2,632 more first-choice votes but failed to reach the 50 percent needed to win.