Justice Sonia Sotomayor said she supports affirmative action in higher education because she believes that alternatives based on geographic or economic status don’t work to ensure a diverse student body.

Sotomayor has said race-conscious programs in the 1970s that opened the Ivy League to minorities were essential to her rise from the Bronx housing projects to her admissions to Princeton and Yale Law School, where she excelled.

In a segment taped for ABC’s “This Week,” George Stephanopoulos asked Sotomayor, the court’s first Latina, about programs that might increase diversity in higher education that would be “less fractious” than the use of race.

She said other programs have not proven to be as successful in diversifying student bodies and that universities should be able to consider race and not just academic measurements.

“What does qualifications mean in an academic setting?” she said. “A place like Princeton could fill their entire beginning freshman class with students who have scored perfectly on undergraduate metrics.

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“They don’t do it because it would not make for a diverse class on the metrics that they think are important for success in life.”

Reminded that President Obama has said his children should not receive special consideration for their race, because of their privileged backgrounds, Sotomayor said: “I agree. But even privileged people will show you dramatic accomplishment that doesn’t go just to grades.”

It is unusual for Supreme Court justices to appear on television, but most make exceptions when they have a book to promote. Sotomayor has actively promoted her memoir, “My Beloved World,” released in paperback this year.

She told Stephanopoulos what she has told other interviewers — that she wrote the book to remind herself of the “real Sonia.”

“I’ve told my friends that if I get too full of myself, I wrote a really thick book so you could hit me over the head with it,” she said.

“The hardcover one,” Stephan­opoulos said.

“The hardcover one, exactly,” the justice replied.

Although the interview aired as the court nears its final day June 30, Sotomayor was not asked about any pending cases.

Sotomayor resisted the suggestion that the members of the court were more “sharp” with one another than in the past.

“Some of my colleagues have a more pugnacious writing style than others,” she said.

Stephanopoulos asked: Meaning Justice Antonin Scalia?

“We’ve got others, too,” she said with a laugh. “And it can be fun, sometimes, to spar.”

Sotomayor also said the photo op of her with Hillary Rodham Clinton at a book-signing by the former secretary of state at a Costco in Virginia was “not planned, I can assure you.”

“A nice lady at the pharmacy counter recognized me,” Sotomayor said, “and we started chatting, and she says, ‘Are you here with the other lady?’ And I said, ‘What other lady?’ And she mentioned Madam Secretary, and that’s how I found out.”