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Ronald S. Lauder, the billionaire cosmetics heir, and Richard D. Parsons, the former chairman of Citigroup, have for decades had their hands in New York City affairs. Mr. Lauder ran a failed bid for mayor and successfully led a campaign for term limits for local elected officials. Mr. Parsons has been a prominent adviser to two mayors.

Now, they are teaming up to try to influence one of the city’s most intractable and divisive debates: how to address the lack of black and Hispanic students at Stuyvesant High School, Bronx High School of Science and the other elite public high schools that use a test to determine admission.

Mr. Lauder this week announced that he was financing a multimillion-dollar lobbying, public relations and advertising effort called the Education Equity Campaign, whose immediate goal is to ensure that Mayor Bill de Blasio’s plan to eliminate the entrance exam does not pass the State Legislature, people involved in the effort said.

More broadly, the two men are trying to make their mark on the future of the system, the nation’s largest, with 1.1 million students.