His announcement of the decision from the bench was businesslike. Signaling deep displeasure, Justice Sotomayor summarized her dissent from the bench, an unusual move that happens perhaps three times a term. She said the initiative put minorities to a burden not faced by other college applicants. Athletes, children of alumni and students from underrepresented parts of the state, she said, remained free to try to persuade university officials to give their applications special weight. “The one and only policy a Michigan citizen may not seek through this long-established process,” she wrote, “is a race-sensitive admissions policy.” That difference, she said, violates the Constitution’s equal protection clause.

“The Constitution does not protect racial minorities from political defeat,” she wrote. “But neither does it give the majority free rein to erect selective barriers against racial minorities.” Justice Ruth Bader Ginsburg joined the dissent.

Justice Sotomayor seemed to mock one of Chief Justice Roberts’s most memorable lines. In a 2007 decision that limited the use of race to achieve integration in public school systems, he wrote, “The way to stop discrimination on the basis of race is to stop discriminating on the basis of race.”

Justice Sotomayor recast the line. “The way to stop discrimination on the basis of race,” she wrote, “is to speak openly and candidly on the subject of race, and to apply the Constitution with eyes open to the unfortunate effects of centuries of racial discrimination.”

Chief Justice Roberts responded in a brief concurrence, saying that affirmative action, and the stigma that he said could accompany it, may do more harm than good. “People can disagree in good faith on this issue,” he added, “but it similarly does more harm than good to question the openness and candor of those on either side of the debate.”

In earlier cases, including one from last June challenging the admissions policies of the University of Texas, the court has said that race-conscious selection can be constitutionally permissible in states that wish to use them. In a concurrence, Justice Antonin Scalia, joined by Justice Clarence Thomas, said those decisions were wrong, and he suggested that they were in peril. He added that the question in Tuesday’s case, Schuette v. Coalition to Defend Affirmative Action, No. 12-682, was laughably easy.

“Even taking this court’s sorry line of race-based admissions cases as a given,” he wrote, “I find the question presented only slightly less strange: Does the equal protection clause forbid a state from banning a practice that the clause barely — and only provisionally — permits?”