WASHINGTON — The Supreme Court has upheld Michigan’s ban on using race as a factor in college admissions.

The justices said in a 6-2 ruling Tuesday that Michigan voters had the right to change their state constitution to prohibit public colleges and universities from taking account of race in admissions decisions. The justices said that a lower federal court was wrong to set aside the change as discriminatory.

Justice Anthony Kennedy said voters chose to eliminate racial preferences because they deemed them unwise.

Kennedy said nothing in the Constitution or the court’s prior cases gives judges the authority to undermine the election results.

Justice Sonia Sotomayor read her dissent aloud in the courtroom Tuesday. Justice Ruth Bader Ginsburg sided with Sotomayor in dissent.