Under ranked-choice voting, it is mathematically possible for the second- and third-place finishers in Tuesday’s Democratic primary to overtake the front-runner — but it will be tough.

It was the city’s first mayoral race using ranked-choice voting, and there was no incumbent running.

After the first round of vote tallying, a relatively conservative male Democrat with a long history in elected office led the pack by nine percentage points, with two female candidates ranked second and third.

In the end, the second-place finisher came from behind to score a narrow victory.

It happened in Oakland, Calif., in 2010. Whether it can happen in New York City in 2021 is a question that has taken on great urgency.

With partial results in on Wednesday afternoon, Eric Adams, the Brooklyn borough president, has 32 percent of first-place votes. He leads Maya Wiley, a former City Hall counsel, by 9 points, and Kathryn Garcia, a former sanitation commissioner, by 12 points.

Because Mr. Adams has almost no chance of garnering more than 50 percent of first-place votes, the ranked-choice playoff process will begin. It is a series of rounds in which the candidate with the fewest first-place votes is eliminated and those votes are transferred to whomever the voter listed in the next slot, until only two candidates remain — at which point the leader wins.

Ms. Wiley’s supporters hope that she can close the gap by picking up enough votes from voters who preferred her to Mr. Adams but did not rank her first. Ms. Garcia’s supporters are hoping for something similar.

But both candidates face steep challenges to overcoming Mr. Adams’s commanding lead. Here is a brief explainer:

Mathematically, yes. Ms. Wiley could win if she makes it to the final round and is ranked ahead of Mr. Adams on around 60 percent of all ballots where neither is ranked first. Ms. Garcia’s threshold in the same situation is a few points higher.

Low. Mr. Adams would have to be enormously unpopular among voters who did not rank him first, and one of the few polls done late in the race showed broader support for him than for Ms. Wiley or Ms. Garcia.

The poll of 800 likely Democratic voters, conducted by Citizen Data and FairVote, a national organization that promotes ranked-choice voting, found that Mr. Adams was the only candidate in the race who was a top-three choice of more than half the voters.

Kathryn Garcia campaigning on the Upper West Side on Tuesday. She was trailing Eric Adams in first-place votes by 12 points on Wednesday afternoon.
Desiree Rios for The New York Times

The poll tracks fairly closely with the actual first-round results reported so far: It showed Mr. Adams with 32 percent and Ms. Wiley and Ms. Garcia both with 18 percent. It was conducted before the race’s chaotic final weekend, when Mr. Adams was criticized for asserting that Ms. Garcia and Andrew Yang, a former presidential candidate, were trying to weaken Black candidates by campaigning together.

That episode may have damaged Mr. Adams and helped Ms. Garcia, but not much, said Rob Richie, FairVote’s president.

“My assumption is that the last three days didn’t change the fundamentals enough to actually change the outcome,” he said.

To give a sense of Mr. Adams’s strength, in a final-round matchup between Mr. Adams and Ms. Wiley based on the voter rankings in the FairVote poll, Ms. Wiley inherited 47 percent of Ms. Garcia’s first-place voters and Mr. Adams inherited 35 percent, but he still beat her by more than 10 points. In a similar matchup between Mr. Adams and Ms. Garcia, she inherited more than 60 percent of Ms. Wiley’s first-place votes but still lost.

Nevertheless, an undaunted Ms. Wiley said on Wednesday that she expected to significantly outpace Mr. Adams in collecting second- and third-choice votes and said she had no plan to concede, “because I’m winning.”

Very rarely. In 128 ranked-choice races in the United States since 2004 where there was no first-round winner, there have been only three occasions where someone trailing by more than eight points after the first round ended up the victor, according to FairVote.

No one trailing by 10 points has ever won, though in the 2018 San Francisco mayoral race, Mark Leno very nearly came from 12 points down to overtake London Breed. Ms. Breed wound up winning by less than a percentage point.

Don Perata, the former head of the California State Senate, led his more progressive opponents Jean Quan by 8.7 percentage points and Rebecca Kaplan by 12.2 points after the first round. But in the elimination rounds, Ms. Quan ended up with 68 percent of the votes from ballots that listed neither her nor Mr. Perata first, and she narrowly defeated him.

There was a big difference, though, between that race and the New York race: Ms. Quan and Ms. Kaplan cross-endorsed each other and co-led an “anybody but Don” attack on Mr. Perata.

“It was really cooperative campaigning between two people who were more on the left,” said Jason McDaniel, an associate professor of political science at San Francisco State University. “It was specifically about going against the perceived establishment candidate.”

Ms. Garcia and Ms. Wiley formed no such alliance. During the campaign, Ms. Garcia seemed open to coalitions with other candidates and explored the possibility of working with Ms. Wiley, in addition to Mr. Yang.

Ms. Wiley said she was invited to campaign with Ms. Garcia and Mr. Yang, but declined because of misgivings about Mr. Yang’s comments at the final debate about people with mental illness.

As of Wednesday afternoon, the in-person votes from about 3 percent of election scanning machines had not been counted yet. Neither had tens of thousands of absentee ballots — a maximum of about 220,000.

But they would have to overwhelmingly favor one candidate to swing the election, and unlike last fall’s Trump-Biden contest, there are no signs of that.

The absentee ballots are widely thought to favor Ms. Garcia over Ms. Wiley because absentee voters tend to be older and Ms. Garcia had an older base, but only moderately.

Those are ballots where every candidate ranked by the voter gets eliminated and thus the ballot no longer directly affects the outcome. The more exhausted ballots there are, the harder it is for a second-place candidate to catch the front-runner. In a race like this one, where there were many viable candidates and voters new to the ranked-choice system might be unwilling to rank a full slate, the possibility of exhausted ballots is high.

We can’t. We don’t know yet where voters ranked anyone other than their first-choice candidate. We don’t know how many ballots are outstanding, let alone how the candidates are ranked on them. That is why the official winner is likely not to be announced until the week of July 12.

Anne Barnard, Nate Cohn, Emma G. Fitzsimmons and Charlie Smart contributed reporting.