Voters in a recent election in Maine. (AP Photo/Robert F. Bukaty)

GORHAM, Maine — On Tuesday, voters here are trying something never done before in the country on this scale: Instead of voting for one candidate in the race for governor, they’re ranking their choices from first to last.

It’s a totally new way of electing politicians in America, one pitched by advocates as the single most transformative way to inject collegiality into today’s hyperpartisan political climate. And if it works, Maine could be a guide for other states considering doing the same.

[Maine primary election results: Governor, Senate and House races]

But it's not clear whether voters will like it, or whether they will vote on the very same ballot to keep ranked-choice voting after years of legal challenges from Republicans trying to get rid of the system voters approved in 2016.

“I didn’t particularly like it,” said Betty Smart of Gorham after testing out the system in the Democratic primary for governor. “I just didn’t feel like I wanted my third and fourth candidates to become governor.”

“It was very easy,” said Virgnia Wilder Cross. “I think it makes sense.”

Here’s how it works: To win a race under ranked-choice voting, a candidate must get a majority of the vote (more than 50 percent) instead of just the most votes (which, in crowded primaries like both sides of Maine’s open governor’s race, could be 25 percent of the total votes).

The candidate with the fewest No.1-ranked votes gets eliminated, and those ballots are credited to the candidates each voter listed as their second choice. The process is repeated until one candidate has a majority.

It’s been compared to an instant primary runoff. And like round two of a primary, advocates say it forces candidates to reach out to a broader group of voters than they would have under the old system. That, they hope, breeds collegiality in politics, which can ultimately help elect candidates who are more willing to compromise.

“It’s risky to be really negative to your opponent,” said Dick Woodbury, a former independent state legislator who helped authored the initial ballot initiative to set up rank-choice voting in Maine.

It wasn’t always clear if Mainers, who approved the new way of voting in 2016, would ever get to use it.

The Republican-controlled state legislature basically repealed the law a year after voters approved it. Some of Maine’s top statewide elected officials opposed it. It’s been caught up in three lawsuits in the past four months alone. A year before the primary, Maine’s highest court ruled that ranking candidates for statewide general elections is unconstitutional.

But advocates of ranked-choice successfully navigated the legal maze so that ranked-choice will be in place in Tuesday in Maine’s crowded Democratic and Republican primaries for governor, as well as one Democratic congressional primary and a Republican state legislative race.

A result of all those legislative challenges and lawsuits: At the same time as voters use the system for the first time, they’ll vote again on whether to keep it. Lawmakers in as many as 20 states and numerous cities are watching what happens here Tuesday to see if they should consider it. It’s currently being used in 11 U.S. municipalities, including San Francisco, and has gained momentum in conservative states like Utah.

Republican candidate for governor Shawn Moody, a front-runner in that primary, was at his hometown polling location urging voters not to use the new system and just mark him as No. 1. None of the Republican candidates for governor support it.

“It becomes more about gamesmanship rather than leadership,” he said of the system, which forces candidates to try to reach out to another candidates' voters.

Underdog Democratic candidates for governor Betsy Sweet and Mark Eves have embraced ranked choice.

They recently ran an ad explaining that they’ll mark each other down as their No. 2 choice and offered their voters to do the same: “You can vote for me first or Betsy second,” Eves says in a campaign ad standing side-by-side with Sweet, “or me first and Mark second,” Sweet interjects.

Both are calculating that forming an alliance can vault one of them to the top of the seven Democratic candidates. It’s the opposite of what campaign consultants would advise, Eves said. They would say to attack the front-runners if you’re behind.

Sweet thinks there’s a populist appeal in ranked-choice voting that speaks specifically to Maine voters, who have a strong independent streak: “It opens the process up to more people and then we don't have the issue of an appointed heir apparent.”

The state Republican Party,  which controls the state Senate and is trying to hold on to the governor’s mansion, has called it confusing and therefore likely to lower turnout, and pointed out that Maine’s constitution prevents ranked choice from being used in statewide general election races. (It says candidates can win with just a plurality of the vote).

“If you’re going to reallocate votes to different candidates, there’s no simple way to explain that,” said Jason Savage, head of Maine’s Republican Party. “It’s going to create a situation where fewer people participate.”

Most of voters trying it out for the first time in Gorham who spoke to The Fix seemed to like it.

“You feel like your vote is going to count more,” said Mederick Black, though he did say the new process took more effort than just choosing one candidate: “It’s a little bit more difficult because you have to make sure everyone is marked in the right column and you don’t mark a guy twice.”

The state’s voting experiment comes comes after eight years of governing by controversial Gov. Paul LePage (R), whose notable past statements include saying “the enemy right now” is “people of color or people of Hispanic origin” and joking about bringing “the guillotine back.” The term-limited LePage won both his elections with less than 50 percent of the vote, a fact that’s top of mind for many Maine voters who support ranked choice.

“If we had ranked-choice voting then,” said Mohamed Omar, a taxi driver in Portland, “then he wouldn’t have won.”

The authors of ranked choice in Maine say this is about improving the election system, not one particular governor. Maine voters approved ranked-choice on the same day Donald Trump was elected president. Their polling suggests it has only gotten more popular in the year and a half since then, and they think if they can win Tuesday’s election and successfully elect two nominees for governor, ranked-choice could be here to stay for most elections in Maine.

“It’s a window of hope at a time when we all really feel there’s something serious that needs to be fixed,” Woodbury said. “There aren’t many people who say: ‘Our political system is healthy right now.’”

This post has been updated.