Extreme-heat warnings haven’t been keeping voters from the polls in the Democratic primary for New York City’s tight mayoral race that is seen as a battle between the party’s center and its progressive left flank .

Polls have former Gov. Andrew Cuomo , 67 years old, as the front-runner heading into the June 24 primary. But democratic socialist Zohran Mamdani , 33, has chipped away at Cuomo’s once-commanding lead.

A poll released Monday by Emerson College Polling predicted Cuomo would stay ahead of Mamdani in the first round of ranked-choice voting but ultimately lose to the Queens assemblyman after the eighth round. The results caused Mamdani’s odds of winning to surge on Polymarket, a popular crypto-based betting platform.

More than 380,000 voters cast early ballots between June 14 and June 22, for primaries that include city-council races and other positions, according to the city’s Board of Elections. Voters who spoke to The Wall Street Journal ahead of Tuesday, the official primary voting day, listed affordability, public safety and Trump administration deportations among their top concerns.

The moderate who changed his mind
Top Choice: Mamdani

Johan Francois , a 36-year-old moderate Democrat, initially leaned toward backing Cuomo. But he changed his mind after the candidate debates.

“He’s just too old,” Francois said of Cuomo. Francois, a tech entrepreneur, said that he was skeptical of Cuomo’s intentions and thinks the former governor is motivated by power.

In the primary, voters get to rank up to five candidates in order of preference. If no candidate hits the 50% threshold in the first round, the candidate with the fewest votes is eliminated, and their votes are redistributed to the second choice. The pattern continues until a candidate hits the threshold.

Francois ultimately decided to rank Mamdani and City Comptroller Brad Lander as his top two choices. Cuomo he ranked at No. 5.

“I intentionally voted Paperboy above Cuomo to send a message,” he said, referring to Paperboy Love Prince , a perennial candidate who often wears clown makeup.

Francois said he was frustrated with establishment Democrats after how they handled the 2024 election.

“The Democratic Party has some waking up to do, and that’s kind of why I picked Zohran,” he said.

The pragmatic Cuomo voter
Top Choice: Cuomo

Liora Michelle Green , a singer and assistant medical-grants manager from the Upper East Side, said she was very aware of the scandal around Cuomo. “Well, maybe plural,” she said. Cuomo was ousted from Albany after a series of sexual-harassment claims that he has denied and accusations of mishandling nursing homes during the Covid-19 pandemic.

But she sees the former governor, who has experience and name recognition on his side, as the most pragmatic choice to take on President Trump.

Cuomo is “very flawed, but nobody’s perfect, and he was able to pass budgets,” Green said. “He is effective; he’s experienced. We need someone strong.”

Green, whose family fled Poland during World War II, choked up while discussing the Trump administration’s aggressive deportations. She said she would like to see Cuomo stand up for New York, as Gov. Gavin Newsom did for California. She wants Cuomo to “protect immigrants who are showing up with their court dates, pushing back against ICE in every way possible,” she said.

“I was iffy about Newsom, I thought he was a bit of a show pony,” Green said. “But he proved his mettle in the recent episode in California, and I think Cuomo can show that same kind of mettle here.”

The couple that has seen a lot on the subway
Top Choices: Mamdani and Lander

Sean Choi and Anne Gerro , a music-festival producer and a business owner, respectively, chose their rankings with the help of an online quiz matching voters with candidates that aligned with their positions. Public safety was a top concern for the engaged couple, both 32, after experiences on the subway.

“There was some crazy guy on the subway who was being a creep in the corner, and then started, like sprinting at us, saying he was going to stab us, and like, followed us off the subway,” Choi said. “Totally just out of his mind.”

Gerro said she would like the future mayor to provide more resources for mental-health care and drug rehabilitation. “The root cause of the boiling up of the mental-health issues, and being able to actually see that in practice, is really just poor access to support services,” Choi said.

Gerro ranked Mamdani in first place, while Choi chose Lander. Cuomo was absent from their rankings. “It’s an immediate no from me,” Choi said, citing the allegations of sexual harassment against the former governor.

The Upper East sider
Top Choice: Cuomo

Mary Jo Keeble has lived on the Upper East Side for over 40 years and voted in “pretty much” every single mayoral election. The decision was simple this time. “I only did one choice: Cuomo,” the 66-year-old apparel merchandiser said.

Keeble said she has always supported the former governor and thought he did a “phenomenal job” keeping New Yorkers updated during the Covid pandemic. “He was not just New York’s governor—he was the governor of America,” she said. “He kept the country calm, basically, in a storm.”

The Upper East sider said she was supportive of Cuomo’s plans to build more affordable housing and increase police presence. “And he’s the only one who can stand up to Donald Trump out of all those guys,” she said.

Keeble decided not to rank any other candidates because few had Cuomo’s level of experience. “I think there’s many of them that aren’t qualified,” she said. “I think there’s many of them that are probably for me personally, too far left, way too far left.”

The ‘young, disillusioned voter’
Top Choice: Mamdani

Christelle Ram , a 27-year-old consultant, sees the mayoral primary as a larger referendum on the Democratic Party . She is backing Mamdani and his platform for an affordable city, in the hopes of moving the party in a more progressive direction. “If this guy wins, it shows that ‘OK, a strong Democratic socialist is attracting young, disillusioned voters,’” Ram said.

“It’s one of the few times I’m actually happy to vote for somebody, instead of just voting for somebody I don’t care about, but the lesser evil,” said Ram, who moved to New York from Orlando, Fla., this year.

Ram said she views Mamdani’s grassroots campaign as more reflective of New Yorkers’ interests than Cuomo’s, which had the support of megadonors including food-delivery service DoorDash and billionaire hedge-fund manager Bill Ackman .

“I’m not interested in voting for a guy that’s Democratic institutional,” she said. “I’m voting for the new guy.”

Write to Jasmine Li at jasmine.li@wsj.com