The opinion is divided. Justice Kennedy wrote the plurality joined by the Chief Justice and Justice Alito. They conclude in their opinion that there is no authority in the federal constitution or in the Court's precedents for courts to set aside Michigan laws that commit to the voters the determination whether racial preferences may be considered in governmental decisions, in particular with respect to school admissions.
...The Chief Justice has filed a concurring opinion. Justice Scalia has filed an opinion concurring in the judgment, joined by Justice Thomas.... Justice Breyer filed an opinion concurring in the judgment. Justice Sotomayor has a dissenting opinion joined by Justice Ginsburg. Justice Kagan took no part.
The plurality opinion stresses that the case is not about the constitutionality or the merits of race conscious admission policies in higher education. Rather, the question concerns whether and in what manner voters in a state may chose to prohibit consideration of such racial preferences.