An article in Harvard Negotiation Law Review points out that courts can order arbitration if both parties agree to it, but cannot control the mechanisms of the arbitration. Therefore, if the company is paying any portion of the arbitrator's fee and the company is not leading in the process, they can elect to not pay the arbitrator's fee. In which case the arbitration fails and the case is dismissed. It appears to be in the plaintiff's interest to prefer mediation over arbitration. In essence, arbitration is broken.
