The lawsuit in federal court is focused on a city policy, dating back to the 1980s, that gives local residents priority in the affordable housing lotteries. Mayor Michael R. Bloomberg expanded the preference to 50 percent of the apartments.

The plaintiffs, represented by Craig Gurian of the nonprofit Anti-Discrimination Center, argue that the policy does not meet federal fair housing requirements. In fact, they argue, the approach exacerbates racial segregation and impedes integration, a finding that Professor Beveridge’s report supported.

“The problem here is that the city takes the luck of the draw and then fixes the deck, and fixes it in a way that it knows will cause a racially disparate impact,” Mr. Gurian said.

Vicki Been, who ran much of the city’s affordable housing program and is now a deputy mayor for housing, rejected the idea that the city’s policy violated federal law or exacerbated residential segregation, observing that the beneficiaries of the city’s housing lottery system were largely black and Hispanic.

“Segregation is a question of choice, and people who chose to live in a neighborhood, we believe, should be able to choose to stay in a neighborhood,” she said in an interview on Monday. “We shouldn’t be telling people you have to move to some other neighborhood.”

She added that one reason for the local preference policy is to address the fear of displacement in communities, particularly when new housing is being built.

“If they fear displacement, they will oppose the housing,” she said. “And the only way that we get a more integrated city is if we have more affordable housing across a wider range of neighborhoods. If people fear that they’re going to be pushed out of their neighborhood, they will not accept housing.”