In recent years, the nationwide Fight for $15 movement has succeeded in persuading several states and cities to raise their hourly minimum wages well above the federal minimum of $7.25. But the effort to ensure a living wage for workers may be headed for a serious setback in the U.S. Supreme Court. Depending on how they rule in a case set for argument next week, the justices could make it much more difficult for millions of workers to secure even the meager wages guaranteed by existing federal law.

On Monday, the day that kicks off the Supreme Court’s new term, the justices will hear arguments in three consolidated cases with far-reaching implications for wage-earners. The cases—Epic Systems Corp. v. Lewis, Ernst & Young LLP v. Morris, and National Labor Relations Board v. Murphy Oil USA, Inc.—are all about whether employers have the right to compel workers go through onerous individual arbitration proceedings in order to bring labor law claims. If the justices answer that question in the affirmative, then the affected workers will—as a practical matter—find it nearly impossible to win back pay in cases involving wage law violations.

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