Nearly ten percent of the cases in the sample concerned credit card disputes. This study finds that since the early 2000s, the share of workers subject to mandatory arbitration has more than doubled and now exceeds 55 percent.Cases ordered to arbitration (in which there are no further proceedings in the court until the case is returned from arbitration);. •. Written contracts may contain an arbitration clause. By using such a clause, the parties agree to arbitrate any future disputes.