New York City—which in the past few decades has witnessed a rising share of majority-Asian neighborhoods , whose residents tend to be foreign-born—is an object lesson in this variation. An analysis of 2010 census data by an NYU-based urban-policy think tank found that the city’s majority-Asian neighborhoods are more economically depressed than those of most other racial distributions: Their average household income of less than $52,000, for example, was less than that of majority-black neighborhoods. That same report found that fewer than a quarter of the adults (25 years or older) living in the majority-Asian neighborhoods at the time had a bachelor’s degree or higher.

Myth 2: Reforming the high-school admissions process will solve the diversity problem.

The bare-bones admissions policy for the city’s eight exam-based, elite public high schools has hardly changed in a half century: A student’s score on a standardized test is the single deciding factor for whether she’s accepted; each school has its own confidential cutoff score, though Stuyvesant is widely thought to be the most selective. Neither a student’s grades nor her previous teachers’ recommendations have a bearing on the decision.

The city has experimented with a string of work-arounds, such as programs that provide exam prep to low-income students and ensure ample test-taking opportunities at underrepresented middle schools. One of de Blasio and Carranza’s latest proposals would basically earmark admission to low-income students who meet a set of rigorous criteria; another would eliminate the test altogether. Opponents argue that in guaranteeing objectivity, the status quo is the only admissions system that protects everyone’s civil rights.

In a court filing responding to the complaint, the city maintains that the model it proposes would have a negligible impact on Asian American representation at the eight schools. Instead, the city argues that by proactively promoting socioeconomic diversity, its plan would elevate the prospects of students of all races—benefiting low-income Asian students just as much as their similarly disadvantaged black and Latino peers. Most of the Asian American students enrolled in the specialized schools are low-income, according to Doug Cohen, a district spokesperson; an earlier district report also indicates that the schools’ Asian American populations tend to be poorer than their classmates of most other racial groups.

“Opponents who seek continued reliance on standardized tests are out of step with the growing body of evidence that confirms that these tests are infected with racial bias and poor predictors of a student's academic potential,” said Kristen Clarke of the Lawyers’ Committee for Civil Rights Under Law, in a press release Tuesday.