Matthew Haag

City Councilman Ben Kallos, who represents the Upper East Side, has led the opposition. “The overall narrative everyone is giving is like, ‘Oh, this is all about NIMBY, this is about a nonprofit and this is about shadows,’” he said. “At the end of the day, this is about an 11-story tower that is somehow 233 feet tall that is a glorified office space for wealthy people.”

Mr. Kallos noted that the Blood Center, under current zoning, could construct a building on the site exceeding 200,000 square feet without additional city approval, more than the amount of space the center plans to occupy in the proposed tower.

Some Upper East Side residents have called for one-way sidewalks. “The stressful part of going anywhere is getting there, because the sidewalks are so narrow,” said City Councilman Ben Kallos, who represents parts of the neighborhood and Roosevelt Island. “There’s no room for distancing, especially when people are walking toward you.”

[F]or many New Yorkers, the most desirable jackpot is not the New York Lotto, but to be selected in the city’s extraordinarily competitive affordable-housing lottery. Tens of thousands of people, and sometimes many more, vie for the handful of units available at a time. Since 2013, there have been more than 25 million applications submitted for roughly 40,000 units....

While the lottery website’s user interface will have an entirely new design, the most significant changes are under the hood. After applicants create profiles stating their household size and household income, which together determine a person’s eligibility, they will be shown apartments that they are most likely to qualify for.

That is a significant change from the old system, in which applicants typically applied to every building on the lottery site without knowing if they were even eligible. That process led some units to receive more than 100,000 applicants, most of whom would never find out that they were ineligible from the beginning.

There were other major problems too, like the site randomly crashing and freezing. City officials said the entire lottery system has been upgraded to improve its usability and stability.

“One of the biggest frustrations was people not hearing if you were accepted and not hearing if you were rejected,” said Luis Daniel Caridad, an assistant director at GOLES, an organization on the Lower East Side of Manhattan that helps people apply for affordable housing. “We’ve been told that it has been fundamentally changed, and we are hopeful.”

For years, the housing lottery only included newly constructed units. When someone moved into one and then left, the vacated apartments did not return to the lottery. Buildings kept their own waiting lists, leading to allegations to those with political connections or who paid bribes could cut in line.

Some of those vacant units will now be entered in the lottery, allowing everyone to be made aware when they become available. Councilman Ben Kallos, who wrote the legislation that requires past rentals to return to the lottery, said the change would eventually bring thousands of units back into the lottery every month.

“Before this, you had waiting lists and you had folks who might be politically connected with an official who knew buildings that had affordable housing,” said Mr. Kallos, a Democrat who represents the Upper East Side of Manhattan. “This means that all the vacant units in the system will be re-rented quickly.” ...