The debate over the new system has been mired in legal challenges and a calcifying partisan edge. Republicans, at first lukewarm on the idea, fought bitterly against it this time around. “It’s the most horrific thing in the world,” LePage, the hyperbole-prone conservative governor, told a local television station the day before the vote. The GOP candidates to replace the term-limited incumbent all railed against ranked-choice, complaining that it was confusing, legally questionable, and sought to fix a traditional first-past-the-post voting method that wasn’t broken.

One of the contenders, Mary Mayhew, told me in April that she might not accept the results under the new system. “It’s an absolute disaster,” she said then. “I think it is likely illegal, and it is incredibly confusing to those who administer the elections and to those who are getting ready to vote.” (Mayhew received just 15 percent of the vote in the GOP primary Tuesday, finishing a distant third behind businessman Shawn Moody, who won the nomination on the first ballot.)

Yet a majority of voters evidently didn’t think it was such a disaster, as they endorsed it on the spot; the unusual try-it-and-decide election on Tuesday was akin to eating at a restaurant and then giving it a positive Yelp review on the way out the door. “The big fear people had was, ‘This is confusing,’” said Jim Melcher, a professor of political science at the University of Maine at Farmington. “I think a lot of people might have been surprised that it was as easy to do as it was.”

Melcher credits the advertising run by advocates of ranked-choice voting, which included tutorials on how the system worked. Voters rank candidates in order of preference, and after the first round, if no one earns a majority, the candidate with the fewest votes is eliminated and the second-choice selections are added to the remaining contenders’ tallies. The process continues, round by round, until someone gets over 50 percent.

The system has been used in Portland, Maine’s largest city, as well as in cities like Minneapolis, Oakland, and Santa Fe, New Mexico. San Francisco has used ranked-choice voting in municipal elections since 2003, and this year, the system contributed to the closest mayoral race in decades. The idea gained momentum in Maine because of the state’s large number of independent voters and the fact that winners of its gubernatorial race in eight of the last 10 elections have done so without capturing a majority of the vote. LePage prevailed with barely over one-third of the vote in 2010, and advocates for ranked-choice voting argue that independent candidate Eliot Cutler would have won had the system been in use at the time.

Proponents have argued that it gives voters more of a voice because by allowing them to rank candidates, it eliminates the need to choose “between the lesser of two evils.” The method ensures that the winner will have majority support without the need for a costly runoff election, in which turnout tends to be lower. It also encourages candidates to appeal to a broader section of voters and discourages negative campaigning, supporters say, by incentivizing rivals to highlight common ground rather than differences.