Conservatives on the Supreme Court on Monday upheld Ohio’s method of purging voters from the rolls after they miss elections.

The court ruled 5 to 4 that Ohio’s process does not violate federal law. The dissenters said it could result in thousands of infrequent voters losing their right to vote.

Unlike many voting cases that come before the court, Wednesday’s case centered not on grand constitutional principles but on interpreting seemingly contradictory directives of federal law.

Beyond the prohibition on removing voters because they failed to vote, the law calls...