GEOFF BENNETT: Tomorrow, voters will head to the polls for the primary that will determine which of the 11 Democrats running will take on New York City Mayor Eric Adams in November.

The race has shaped up as a contest between a well-known establishment figure seeking a political comeback and a rising young Democratic socialist who has mounted an unexpected challenge.

William Brangham has this preview.

WOMAN: Have you heard of Zohran Mamdani before?

WILLIAM BRANGHAM: It's a question many New Yorkers can answer affirmatively now,ever since Zohran Mamdani, the 33-year-old assemblyman from Queens, surged to become one of the biggest surprises in this New York mayoral primary.

WOMAN: We need a mayor who's going to fight to lower the cost of living for New Yorkers and actually stand up to Trump.

ZOHRAN MAMDANI (D), New York Mayoral Candidate: Are we ready to stand up and fight back?

(CHEERING) WILLIAM BRANGHAM: The young Democratic socialist has risen dramatically in polls in the last few months, driven by an army of volunteers and a charismatic social media presence.

ZOHRAN MAMDANI: Who knew that policies like universal childcare, rent freeze, and taxes on mega-corporations were popular?

We did.

SAMAN WAQUAD, Zohran Mamdani Volunteer: To me, Zohran is the real deal.

He's not just words.

He's action as well.

And does he get it right all the time?

Nobody does, right?

But I think he is our best chance at having a New York City that is livable and affordable for everyone.

WILLIAM BRANGHAM: In Brooklyn, volunteers with the Service Employees International Union are knocking on doors for Mamdani's main rival, a candidate who needs little introduction to New Yorkers.

WOMAN: Yes, what we're going to give her is this, saying that we support Andrew Cuomo.

WILLIAM BRANGHAM: Andrew Cuomo was governor of New York for a decade, before resigning in 2021 after a flurry of sexual harassment allegations.

The moment he entered the mayor's race, he was instantly the presumptive front-runner, riding high on name recognition and support from many unions and local officials.

ANDREW CUOMO (D), New York City Mayoral Candidate: We are here because we know we can turn New York City around.

We have already showed what leadership and confidence and unity can do.

WILLIAM BRANGHAM: Cuomo's message, that he's got years of experience to bring to the office starting on day one, resonates with a lot of New Yorkers.

ALDANIA REYES, Andrew Cuomo Volunteer: I saw the great job that he did during COVID.

I said, you know what, this is my guy.

I got to go up there for him.

TRIP YANG, Democratic Strategist: You have different ideologies, very different backstories between the two front-runners, but also it's a reflection of what do voters, as consumers in the political market, what do they really want?

WILLIAM BRANGHAM: Trip Yang is a Democratic strategist in New York.

He's not affiliated with any of the mayoral candidates.

TRIP YANG: Andrew Cuomo is running on managerial experience: I know how to run a state.

I can therefore govern the largest city.

WILLIAM BRANGHAM: No training required.

TRIP YANG: Right.

Zohran Mamdani is banking that New York City Democratic voters view an election for mayor as a sales pitch, not a job interview.

They want to be inspired.

WILLIAM BRANGHAM: What is it about Mamdani that you find appealing?

STEPHEN FRAILEY, Democratic Primary Voter: I think he's very smart and he's run a good campaign.

And I think he has a kind of charisma that will unite the city.

WILLIAM BRANGHAM: Who would you like to see win?

SANDY ADELSBERG, Democratic Primary Voter: Andrew Cuomo.

WILLIAM BRANGHAM: How come?

SANDY ADELSBERG: Because I think he's a terrific politician.

I think he understands how to run things.

He's a tough guy.

In today's soft world, you're not allowed to be tough any longer.

That's what's going on.

Everybody has to just be milquetoast.

And Cuomo will never be milquetoast.

WILLIAM BRANGHAM: That reputation for toughness and experience also comes with a heavy load of political baggage, something Mamdani skewered him for in a recent debate.

ANDREW CUOMO: To put a person in this seat at that -- at this time with no experience is reckless and dangerous.

ZOHRAN MAMDANI: To Mr. Cuomo, I have never had to resign in disgrace.

I have never cut Medicaid.

I have never stolen hundreds of millions of dollars from the MTA.

I have never hounded the 13 women who credibly accused me of sexual harassment.

PATRICK GASPARD, Center for American Progress: In many ways they represent the two poles that are vying for the direction and the compass of the national Democratic Party.

WILLIAM BRANGHAM: Patrick Gaspard has advised multiple New York mayors and served as political director for President Barack Obama.

He says the argument that Mamdani is too inexperienced, a critique Obama faced as well, is cutting both ways in this race.

PATRICK GASPARD: Zohran Mamdani has attempted to make an argument about how that experience hasn't always served the interest of working people, right?

Because this experience question is a double-edged sword.

I think that Andrew Cuomo came into this race and drew a picture of a kind of a dystopian New York that interestingly was not dissimilar to the picture that Donald Trump drew of New York.

Everything's falling apart, and I alone can save you from it.

WILLIAM BRANGHAM: And, of course, the specter of President Trump looms large in this campaign, with candidates weighing in on everything from immigration policy to the recent bombing of Iran.

ANDREW CUOMO: I know how to deal with Donald Trump because I have dealt with him before.

ZOHRAN MAMDANI: I am Donald Trump's worst nightmare as a progressive Muslim immigrant who actually fights for the things that I believe in.

PATRICK GASPARD: Democrats, writ large, but especially Democrats in New York, are looking for pugilists against Donald Trump, are outraged by the violations of the Constitution, and Democrats want to see us fighting against him.

WILLIAM BRANGHAM: That fight spilled overtly into the campaign last week, when City Controller and mayoral candidate Brad Lander was arrested by federal agents while escorting a man from court.

BRAD LANDER, New York City Comptroller: You don't have the authority to arrest U.S. citizens.

Asking for a judicial one.

WILLIAM BRANGHAM: Both Cuomo and Mamdani condemned the arrest.

But Trump's fingerprints have also been on this race because of his intervention for a candidate who's not on Tuesday's ballot.

Last September, New York City Mayor Eric Adams was indicted on federal corruption charges.

PROTESTER: Adams out now!

WILLIAM BRANGHAM: But then the Trump administration dropped that prosecution as Mayor Adams agreed to help Trump's hard-line approach to immigration.

ERIC ADAMS (D), Mayor of New York: I wanted to run in a Democratic primary, but I have to be realistic.

WILLIAM BRANGHAM: In April, facing plummeting approval ratings, Adams said he'd run for reelection as an independent.

TRIP YANG: It doesn't matter what happens in Democratic primary.

If it's Andrew Cuomo as the nominee and Zohran Mamdani running on a third party, or vice versa, Eric Adams has no shot.

Party loyalty in November reigns supreme.

WILLIAM BRANGHAM: But there's another major factor in this race, and that is that voters are using what's called ranked-choice voting, which allows them to choose up to five different candidates ranked in order of their preference.

NARRATOR: If one candidate gets more than 50 percent of everyone's first choice votes, they win the election right away.

WILLIAM BRANGHAM: But if no one hits that threshold, the lowest ranked candidate is eliminated, and anyone who chose that person will have their vote transferred to their next ranked candidate.

These rounds of tabulation continue until there are only two candidates left and whoever has the most votes wins.

The process has also led candidates like Mamdani and Lander asking their voters to rank each other on their ballots so that, if one loses, the other benefits.

ZOHRAN MAMDANI: Let's do it together.

ZOHRAN MAMDANI AND BRAD LANDER: We're cross-endorsing.

WILLIAM BRANGHAM: But as the race has tightened with Mamdani's rise, a tidal wave of super PAC money has come in to bolster Cuomo, including more than $8 million from billionaire and former New York Mayor Michael Bloomberg.

NARRATOR: Zohran Mamdani, a risk New York can't afford.

WILLIAM BRANGHAM: Mamdani would be the city's first Muslim mayor, and he's been criticized for calling Israel's actions in Gaza a genocide.

In recent days, Mamdani says he's received death threats, calling him a terrorist.

Regardless of Tuesday's outcome, Cuomo says he will also run as an independent in the general election, a move that Mamdani could also consider.

So, a second round is possible come November.

For the "PBS News Hour," I'm William Brangham in New York City.