“I have serious concerns about how this is going to be implemented, and I believe it is fraught with the vulnerability for error,” she continued. “That in and of itself may call into question the results.”

Mayhew is facing businessman Shawn Moody and two top Republicans in the state legislature—House Minority Leader Ken Fredette and Senate Majority Leader Garrett Mason, who leads a caucus that voted to appeal a judge’s ruling last week ordering the state to implement ranked-choice voting. All four Republicans have criticized the format, as has the state party.

“The system itself is more expensive, it’s going to suppress votes, and we think it’s just a bad idea,” Jason Savage, executive director of the Maine Republican Party, said. “We’re concerned about a constitutional crisis of months of court challenges to results that end up with us not knowing who our candidates are.”

Ranked-choice voting, which cities like San Francisco, Minneapolis, and Portland, Maine, use to elect their mayors, has been likened to an “instant runoff”: Instead of selecting just one candidate, voters rank their choices in order of preference. If no candidate receives a majority of first-place votes, the candidate with the fewest votes is eliminated, and whoever their voters chose as their second choice is added to the tally of the remaining contenders. That process continues until there are only two candidates left, and the one with the most votes wins.

The idea had been bandied about for years in Maine, a state where the frequent viability of independent candidates has led to gubernatorial campaigns in which the winner had received less than a majority mandate in eight of the last 10 elections. It gained momentum after LePage won his first election in 2010 with just 37.6 percent of the vote; advocates for ranked-choice voting argue that independent candidate Eliot Cutler would have prevailed had the system been in use then.

Proponents held up ranked-choice voting as a remedy for the increasing vitriol of elections in Maine, which for a long time had viewed itself as removed from the partisan rancor that dominated national politics. “The quality of our campaigns has deteriorated,” John Brautigam, legal counsel and senior policy adviser for the League of Women Voters of Maine, said, “and maybe ranked-choice voting holds a way to restore some of that special quality to our democracy here in Maine, to preserve decent relationships among candidates and minimize the negativity, and encourage broader outreach by campaigns to all possible voters.”

“People have been focused on LePage, because he’s been the most visible example of it,” Brautigam said, referring to a governor whose impolitic pronouncements and battles with the state legislature have made national headlines for years. But, he said, the problem went beyond merely the Republican in power.