That's the question asked by law professor Ann Hodges in Trilogy Redux: Using Arbitration to Rebuild the Labor Movement. Here is the abstract:
The Supreme Court is in the midst of a revolution in arbitration jurisprudence comparable to that reflected in the Steelworkers Trilogy in 1960. While the Trilogy was hailed as a major accomplishment in labor relations, the current revolution is devastating the rights of nonunion workers and consumers. The Court’s evisceration of the class action through approval of waivers in unilaterally imposed arbitration agreements has forced employees and consumers to individually arbitrate legal claims. While plaintiffs’ attorneys are quick to file class actions in court, they are far less interested in individual arbitration cases. This development may provide an opportunity for labor unions to step in and offer assistance to workers with these claims. This paper discusses several ways that unions might capitalize on this development to grow the labor movement, considering the advantages and disadvantages of possible options. Whichever is chosen, however, it is crucial that providing representation to workers with legal claims is only one piece of a larger strategy. The strategy must be designed to build a worker-driven movement capable of meeting the needs of 21st century workers and providing balance to the power of 21st century wealth. To achieve this objective, unions cannot be merely service organizations for members. Instead, they must be part of a broader movement for workplace equality.