PORTLAND, Maine (AP) — Maine residents rejected a delay legislators had sought to implement ranked-choice voting, allowing the system used for the first time in Tuesday’s primaries to also be used in federal elections in November.

The election overhaul allows voters to rank their candidates from first to last on the ballot. If there’s no majority winner, then there are additional voting rounds.

Republican businessman Shawn Moody won Tuesday’s Republican primary, gaining a majority of vote to eliminate the need for additional rounds of voting. No clear majority winner had emerged in the Democratic primary.

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If the Democratic result holds when all of the votes are counted, there would be additional rounds of vote tabulations next week, as election officials eliminate last-place candidates and reallocate votes. The winner of that race may not be known for at least a week.

Supporters say the system ensures a majority winner, eliminates the impact of spoilers and encourages civility in campaigns. Opponents have said it’s confusing and doesn’t square with the Maine Constitution. It is already used in 11 local jurisdictions.

Voters used it to sort through a crowded gubernatorial field that includes 11 Democratic and Republican candidates, as well as a Democratic congressional primary and a Republican legislative primary.

“I’m interested in people working together. I think it’ll move us in the direction of people working together,” said voter Linda Misener, who cast a “yes” ballot in Portland.

Many voters on Tuesday had a firm grasp of the ballot.

“It’s pretty easy to do, despite the negative publicity. I can count to seven, and they can do the math on the other end,” said David Kuchta, of Portland, referring to the number of candidate he ranked in the Democratic gubernatorial primary.

The system has faced legal challenges, in addition to legislative hurdles. But Maine’s highest court in April cleared the way for voters to use the ranking system.

Critics included Republican Gov. Paul LePage, who announced Tuesday that he probably wouldn’t certify primary elections results under the system. His announcement was largely symbolic. Democratic Secretary of State Matthew Dunlap said such an act wouldn’t change anything.

The system works like this: A candidate who scores a majority of votes wins. If there is no majority, then the last-place candidate’s votes are reallocated and the votes are tabulated again.

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State lawmakers last fall decided to delay ranked-choice voting until 2021, when it would be repealed unless allowed by a constitutional amendment. But that was nullified by a second statewide vote on Tuesday.

The decision means Mainers will be able to use ranked-choice voting for future primary elections and U.S. House and U.S. Senate elections in November. It won’t be used for legislative and gubernatorial general elections because of state constitutional concerns.

The voting system survived a legal challenge by the Maine Senate on constitutional grounds.

Maine Republicans wanted to be exempted from ranked-choice voting in their primary, but a federal judge rejected the request for an injunction last month.

On Tuesday, several Democratic voters pointed to the election of LePage in 2010 for supporting the voting system. LePage won without a majority in a multi-candidate race in which Democrats torn between two other candidates split their votes.

A few were surprised to learn that new voting system won’t apply to that governor’s race in November, even if residents agree to carry it forward.

“Things take time, unfortunately. It’d be nice if thing went faster,” said Carmine Terracciano of Portland. “You gotta start somewhere.”

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Associated Press writers David Sharp and Marina Villeneuve in Portland contributed to this report.

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