WASHINGTON — The Supreme Court’s conservative justices signaled Tuesday they are likely to uphold a Michigan voter initiative that forbids its state universities from granting “preferential treatment” to applicants because of their race.

The Michigan measure was modeled on a law adopted by California’s voters in 1996, but it was struck down last year by a federal appeals court in Ohio. Those judges said the state’s voters, most of whom are white, had taken away a special admission policy that helped bring racial diversity to the campuses.

Much of the hourlong argument turned into a debate on what is meant by equal treatment under law. The conservatives said that ignoring a student’s race constituted equal treatment, while the liberals said that ignoring race denied them true equality.

A majority of the justices have been skeptical of race-based admissions policies, and they seemed ready to uphold the Michigan measure.

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