When New Yorkers vote in the June mayoral primaries, they will get to pick up to five candidates, in ranked order of preference.

No one knows exactly how the system, known as ranked-choice voting, might affect the outcome, but plenty of voters were still confused about how it worked when it was used in a special City Council election in Queens last week.

The new approach to voting was expected to make candidates refrain from attacks, but the friendly sheen among them is starting to wear off. They are more directly criticizing one another at forums, seeking to highlight their differences.

And a new Republican candidate joined the fray. Here are some key developments in the race:

The candidates began to take the gloves off

The conventional wisdom around ranked-choice voting is that candidates should avoid insulting their opponents for fear of alienating those opponents’ supporters. After all, voters’ second choices could be critical.

But now, less than five months before Primary Day, several of the mayoral candidates appear to be making a more straightforward calculation: The time for sharper contrasts has arrived.

Maya Wiley, a former counsel to Mayor Bill de Blasio, laced into Andrew Yang over his campaign’s use of nondisclosure agreements, which he said had been discontinued, and highlighted complaints about the culture on his presidential campaign. Shaun Donovan pointedly raised Raymond J. McGuire’s Wall Street background. Mr. McGuire shot back by calling Mr. Donovan “Shaun Obama,” a dig at the former federal housing secretary’s regular mentions that he worked under President Barack Obama. Scott M. Stringer issued barely veiled rebukes of Eric Adams and Mr. Yang over their in-person campaigning during the coronavirus pandemic.

And at a candidate forum on homelessness, Dianne Morales contrasted her experience with Mr. Stringer’s, calling him out by name.

“Unlike Scott, I’ve actually been talking to the people that are homeless for the last 15 years,” Ms. Morales said. “I’ve been doing the work.”

In the scheme of American political discourse, these were, at most, mild exchanges. But they reflect a growing recognition that there is limited time to break out of the pack — and that candidates cannot count on anyone else to negatively define their chief rivals for them.

On Sunday, though, advisers to two top candidates certainly tried: Aides to Mr. Yang and Mr. Stringer broke into a sharply personal Twitter exchange tied to the issue of support from the real estate industry.

The first ranked-choice election confused voters

It was the debut that wasn’t.

A little-known special election in Queens became the testing ground for New York City’s ranked-choice voting system last week, the first time the new system was used ahead of the mayoral primary.

How would voters welcome the ability to rank up to five candidates instead of picking just one? Would the system, which could trigger multiple rounds of vote tabulations, be a stumbling block for the traditionally dysfunctional Board of Elections?

In the end, however, one candidate, the former councilman James Gennaro, seemed poised to receive more than 50 percent of the vote, making him the likely winner in the City Council’s 24th District. Were he to receive less than 50 percent, the last-place candidate would be eliminated, and that candidate’s votes would be redistributed to the second choices listed on the ballots of voters who favored the eliminated candidate. The process would be repeated until one candidate reached a majority of the vote.

Still, the election served as a dry run for a new voting method that will require significant public education.

Some voters said they were unfamiliar with exactly how ranked-choice worked, despite being contacted by the campaigns or receiving mailers explaining it.

“It didn’t really quite sink in, and I really liked one candidate, so I just voted for him,” said Kanan Roberts, 71, who voted for Mr. Gennaro.

Other voters were more aware of its intricacies and appreciative of the ability to vote for several candidates.

“If you want to take a risk on a candidate that you don’t know whether they have a realistic shot of winning, but they’re your candidate of choice, they don’t have to be a spoiler anymore under ranked-choice voting,” said Peter Sullivan, 39. “You can pick them first, then pick the safer, ‘electable’ candidates second and third.”

Could the city’s first Hispanic mayor be a Republican?

A key question in the mayor’s race is which Democratic candidate will win support from the city’s sizable Hispanic community. Ruben Diaz Jr., the Bronx borough president who is of Puerto Rican heritage, was viewed as a top contender before he dropped out of the race last year.

But what if that candidate turned out to be a Republican?

Fernando Mateo, who was born in the Dominican Republic, announced his mayoral campaign in an unusual video on Facebook last week where he shaved his head — a nod to new beginnings as New Yorkers look forward to the end of the pandemic.

“I wanted to show my beauty,” he said in an interview. “I’m the cutest candidate in the race.”

Mr. Mateo runs a restaurant, Zona de Cuba, in the Bronx and has led trade groups for livery drivers and bodega owners. He has been involved in politics for years but was also linked to a scandal over Mayor Bill de Blasio’s fund-raising.

His campaign website boasts that he was once named “One of the Five Most Influential People in the Country” by The New York Times. That article, in 1994, reflected the results of a survey of senior executives shortly after Mr. Mateo had created a program to trade guns for toys.

Mr. Mateo said he wants to to revisit bail reform, keep the jail on Rikers Island open and “re-fund the police” — instead of defunding the department. He distanced himself from former President Donald J. Trump and said he was embarrassed by the riot at the U.S. Capitol.

“That’s not what the Republican Party is all about — that’s not what we’re about,” he said. “I’m an urban Republican. I believe in cities and immigration. I don’t believe in hatred.”

There has been some debate over whether the city has already had a Hispanic mayor. John Purroy Mitchel, who was mayor from 1914 to 1917, was descended from Spanish nobility.

A homeless expert on homelessness grills the candidates

Ten mayoral candidates took part in a Zoom forum on homelessness Thursday night, but the standout speaker was one of the moderators: a homeless man who goes by the name Shams DaBaron.

Mr. DaBaron, 51, who emerged last fall as the self-appointed spokesman for homeless men battling to remain in the Lucerne Hotel on the Upper West Side over objections from neighbors, demonstrated a grasp of the issues that comes from having lived them.

When the candidates were asked if they would disband the police unit that tries to move homeless people from street to shelter, one of them, Loree Sutton, said she would not, and that she would “team up police with peer-to-peer counselors.”

Mr. DaBaron explained to her how “outreach” is practiced by the police. “Where they were telling me they were going to help me, and I submitted to the help, I ended up in handcuffs,” he said. “They brought me to a police station, made me take off my sneakers and threw me into a cell and then threatened to give me a ticket unless I entered the shelter system.”

In response to a question about plans for the unsheltered people the city has placed in hotels during the pandemic, Shaun Donovan, a longtime government official, offered a mini-filibuster touting his college volunteering, his work with veterans under Mr. Obama and the importance of “reimagining the right to shelter as a right to housing.”

Mr. DaBaron asked his co-moderator, Corinne Low of UWS Open Hearts, an organization that supports shelters on the Upper West Side, to pose the question to Mr. Donovan again, suggesting that the candidate had not really answered it.

Mr. DaBaron, who tweets as Da Homeless Hero, garnered some raves on Twitter.

One person praised him for “not letting any candidate talk about anything other than the content of the questions”; another suggested he might consider running for office.

“@homeless_hero for mayor!” the user @SoBendito wrote.

Maya Wiley chose Gracie Mansion over her own TV show

Two candidates had to abandon high-profile jobs as television pundits to run for mayor: Ms. Wiley, a legal analyst at MSNBC, and, Mr. Yang, a commentator at CNN.

But for Ms. Wiley, the sacrifice might have been more substantial.

Speaking to more than 170 women on a “Black Women for Maya” virtual event on Wednesday, Ms. Wiley said she had an opportunity to audition to replace Joy Reid’s weekend talk show “AM Joy” as Ms. Reid was being promoted to host her own prime-time show.

Ms. Wiley, a civil rights lawyer, said that she “loved MSNBC” because “it felt like a family” and that she was proud of being a Black woman who was being paid to deliver legal analysis.

After Ms. Reid “broke a Black glass ceiling” and received her own prime time show, “MSNBC knew one thing; They’d better put somebody Black in that seat, they knew it,” Ms. Wiley told the audience.

She said that she decided not to take the network’s offer of an audition, because “as much joy and as big a paycheck as that MSNBC slot would have been, I knew we had so many treasures that could fill that seat.” She ultimately decided that “in this moment, to me, the greatest gift and privilege would be making people’s lives better.”

Mr. Yang said he made a similar deliberation when deciding to leave his position at CNN.

“I was very appreciative of my time at CNN. I made a lot of friends,” Mr. Yang said. “But I’m someone who is looking to help people at scale, and New York City is in a lot of pain right now. I’m more of a doer than an analyst.”