WASHINGTON — The Supreme Court today upheld Michigan’s ban on using race as a factor in college admissions despite one justice’s impassioned dissent that accused the court of wanting to wish away racial inequality.

The justices said in a 6-2 ruling that Michigan voters had the right to change their state constitution in 2006 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.

The decision bolstered similar voter-approved initiatives banning affirmative action in education in California and Washington state. A few other states have adopted laws or issued executive orders to bar race-conscious admissions policies.

Justice Anthony Kennedy said voters chose to eliminate racial preferences, presumably because such a system could give rise to race-based resentment. Kennedy said nothing in the Constitution or the court’s prior cases gives judges the authority to undermine the election results.

“This case is not about how the debate about racial preferences should be resolved. It is about who may resolve it,” Kennedy said.

In dissent, Justice Sonia Sotomayor said the decision tramples on the rights of minorities, even though the amendment was adopted democratically.

“But without checks, democratically approved legislation can oppress minority groups,” said Sotomayor, who read her dissent aloud in the courtroom Tuesday.

Judges “ought not sit back and wish away, rather than confront, the racial inequality that exists in our society,” Sotomayor said.

Justice Ruth Bader Ginsburg sided with Sotomayor in dissent.