Former Gov. Andrew M. Cuomo, seeking to gain ground in the New York City mayor’s race, this week took aim at his main rival by proposing a law to reserve coveted rent-stabilized apartments for people of lesser means.

The proposal is an attempt to seize momentum on one of the campaign’s top issues — the housing crisis — and could affect nearly one million homes, or about 40 percent of the city’s rental market.

It’s also part of a continuing attack on the front-runner in the race, Assemblyman Zohran Mamdani, who pays $2,300 a month for a rent-stabilized one-bedroom apartment in Astoria, Queens.

Mr. Cuomo has said that Mr. Mamdani, who earns $142,000 a year as a lawmaker, should give up his apartment so a homeless family can move in. Mr. Mamdani has said Mr. Cuomo is being petty and vindictive.

City officials and housing experts have long debated how to make sure lower-cost housing goes to people who might need it the most. But Mr. Cuomo’s proposal, which he is calling “Zohran’s Law,” prompted fierce criticism from renters’ groups and skepticism from advocates for landlords and even some of the former governor’s onetime allies.

Here’s what to know.

How would the law work?

Mr. Cuomo’s proposal would allow people to move into rent-stabilized apartments only if they would be spending at least 30 percent of their earnings on rent.

If, for example, an apartment rents for $2,500 a month, which amounts to $30,000 per year, the new household’s annual income could not be more than $100,000, Mr. Cuomo said. People could presumably use guarantors or vouchers to qualify for apartments that cost more than their own income can cover.

But the maximum income Mr. Cuomo’s law would allow is the current minimum requirement for many landlords, who worry about choosing tenants who might struggle to pay rent that is more than 30 percent of their income. That tension could drastically reduce the pool of eligible renters for each unit.

Incomes and eligibility would be verified by the landlord only at the time of move-in, according to Mr. Cuomo’s spokesman, Rich Azzopardi.

Mr. Azzopardi said that the program would be overseen by the city’s Housing Department. He asserted that the cost to taxpayers would be “de minimis,” since the city already does this kind of vetting for people moving into city-subsidized housing.

Changes would most likely take place slowly. Mr. Cuomo’s proposal would apply only to new tenants; the median rent-stabilized household stays put for about eight years, compared with three years for tenants in unregulated apartments.

Mr. Cuomo, who told The New York Times that he pays about $8,000 a month for a market-rate apartment in Manhattan, said in a news release that the goal of the law is to “protect” rent-stabilized homes from the wealthy and “high-income individuals” who are not “truly in need.” Mr. Mamdani’s salary would land him in the 90th percentile of the city’s earners in 2022, according to an analysis by the city’s Independent Budget Office. The city’s median household income is $77,000.

Still, even many high earners say they feel middle-class because they struggle to afford basic living expenses like housing and child care.

Do most current tenants meet the requirements?

Of the nearly one million rent-stabilized households, about four in 10 spend over 30 percent of their income on rent, and would hypothetically qualify under Mr. Cuomo’s rules if they were moving into the same apartment they live in today.

But that leaves out much of the other 55 percent — more than half a million households. (A portion of these people may live in city-subsidized affordable housing, and would presumably be outside the scope of Mr. Cuomo’s proposed law.)

Rent-stabilized households tend to earn less and pay less in rent than market-rate households.

Still, more than 40 percent of rent-stabilized households earn at least $75,000, according to an analysis of city housing data by the Citizens Budget Commission, a nonprofit fiscal watchdog.

About 7 percent of rent-stabilized households earn between $150,000 and $200,000 and pay a median rent of about $1,870. Another one in 10 rent-stabilized households earn at least $200,000, according to the analysis, and their median rent is $2,200.

There is a high need for affordable housing among people not living in rent-stabilized units. About 40 percent of households that rent at market rates are rent-burdened, according to city data, meaning they spend more than 30 percent of their income on rent.

A 2021 paper by the New York University Furman Center, a housing-focused research group, found that rent regulation tends to benefit higher earners more than other income groups over time.

Basha Gerhards, the senior vice president of planning for the Real Estate Board of New York, an influential industry group, said it was “well documented” that “the benefits of rent regulation are not well targeted.”

On the other hand, many rent-stabilized homes are subsidized by the city, according to the Furman Center, and already restricted to people with lower incomes. About 300,000 older rent-stabilized homes fall into this category.

It might be a big undertaking.

Filling vacant affordable apartments quickly has been a constant struggle for the city.

The Furman Center paper said that any scheme trying to means test rent-stabilized apartments “would create significant administrative challenges.”

Rafael Cestero, who was housing commissioner under Mayor Michael R. Bloomberg, said that the “bureaucratic burdens” to oversee means testing are “overwhelming.”

“I have long thought that if there was a way to do some kind of means testing, then you could really argue that the system is getting to the people who need the housing the most,” said Mr. Cestero, now the chief executive of the Community Preservation Corporation, a nonprofit that lends money to owners of older rent-stabilized buildings. “That doesn’t mean it’s feasible or doable, and that’s the real issue.”

It could also be an added burden for landlords, said Kenny Burgos, the chief executive of the New York Apartment Association, an advocacy group for rent-stabilized landlords.

Many owners already check incomes as part of an apartment application process, but sending information to the government presents an added complication. Also, owners might have to try harder to find tenants who are rent-burdened, but not so burdened that they won’t be able to pay the rent.

In the meantime, the apartment will most likely sit empty and the landlord won’t collect any rent, Mr. Burgos said.

How are people reacting to the proposal?

Mayor Eric Adams, who is running against Mr. Cuomo and Mr. Mamdani, said this week that “rent-stabilized apartments, low-income apartments” should be for “low-income people.” But a spokesman for the mayor also called the latest proposal “political theater.”

Mr. Mamdani, who soundly beat Mr. Cuomo for the Democratic nomination for mayor in June, was asked about the law this week. He responded: “How many New Yorkers would have their lives upended by a former governor who is responding to the fact that he was handily beaten by a tenant of a rent-stabilized apartment?”

Representative Ritchie Torres, a Bronx Democrat who supported Mr. Cuomo in the primary, said on X that Mr. Cuomo’s plan “would lead to the mass displacement of working-class and middle-class New Yorkers.”

“Market-rate housing is so prohibitively expensive that even the most solidly middle-class families can scarcely afford it,” he said. “Add to that the crushing cost of utilities, insurance, child care … and the combination is overwhelming.”