The last time New Yorkers went to the polls, they had to contemplate a governor’s race and a slew of congressional races in the critical 2022 midterm elections.

But there was one variable that they did not have to deal with: ranked-choice voting, which had been used the previous year in the mayoral election.

For the City Council races on the ballot this year, ranked-choice voting returns for the June 27 primaries, with early voting beginning Saturday, June 17.

Here’s what you need to know about the voting system:

The voting system, overwhelmingly approved by the city’s voters in 2019, is used in primary and special elections for mayor, public advocate, comptroller, borough president and the City Council.

Under ranked-choice voting, voters can list up to five candidates on their ballots in order of preference.

If a candidate receives more than 50 percent of first-choice votes in the first round, they win.

If no candidate does, the winner is decided by a process of elimination: The lowest-polling candidate is removed from each round, and their votes are reallocated to whichever candidate those voters ranked next until only two candidates are left. The candidate with the most votes wins.

That might sound complicated. But all you need to know as a voter is this: Rank your favorite candidate first and then pick as many as four other choices, in order of preference.

Maybe.

Mr. Adams had expressed doubts about ranked-choice voting, but it might have helped him win — even if the process was messy.

Initially, early unofficial results showed Mr. Adams with a narrow lead. But then election officials announced they had miscounted the ballots. A new tabulation still found that Mr. Adams had collected the most first-round votes, but he was not declared the winner until weeks later, when voters’ secondary choices were tabulated.

Under the old system, Mr. Adams would have faced a runoff because he did not receive at least 40 percent of votes. In a runoff, he would have faced his closest first-round rival in the 2021 Democratic primary: Maya Wiley, a lawyer and MSNBC contributor. Voters would have faced a clear choice between two candidates, and it is not clear who might have won.

But after voters’ ranked choices were considered, Ms. Wiley was eliminated, and in the last round, only Mr. Adams and Kathryn Garcia, the city’s former sanitation commissioner, remained.

Mr. Adams won the primary by a slim margin: only 7,197 votes. The ranked-choice system also aided Ms. Garcia; she was in third place after the initial count of first-place votes, but moved up to second as other candidates were eliminated, and their supporters’ votes were reallocated.

Every member of the 51-member City Council is running to keep their seat, including candidates who won two years ago under unusual rules that were part of the City Charter.

Less than half of races are being contested, and of those, 13 races feature more than two candidates — making ranked-choice voting necessary.

The most interesting of those races is in Harlem, where the current council member, Kristin Richardson Jordan, a democratic socialist, recently bowed out of the race.

Proponents say the system enables people to more fully express their preferences and to have a greater chance of not wasting their vote on a less popular candidate. Voters can leave a candidate they really don’t like off their ballot and make sure their vote helps one of their opponents.

There is also evidence that ranked-choice voting encourages more candidates to run, especially women and people of color, and that it discourages negative campaigning, since candidates are no longer competing for a person’s only vote.

Candidates sometimes cross endorse each other to boost like-minded allies. Some political experts believe that if Ms. Garcia and Ms. Wiley had cross-endorsed each other in the primary, one of them would have become New York City’s first female mayor.

Ranked-choice voting is used in Maine and Alaska, and in dozens of cities including San Francisco and Minneapolis. Opponents believe that it confuses many voters, and may discourage some to vote.

Yes.

Just days before early voting started, two Democratic candidates in the competitive City Council race in Harlem endorsed each other: Yusef Salaam, an activist who was wrongly imprisoned in the Central Park rape case, and Al Taylor, a state assemblyman.

The move appeared aimed at stopping Inez E. Dickens, a Democratic state assemblywoman who formerly held the Council seat.