In many markets, disagreements are settled using arbitration. We examine this understudied form of dispute resolution in the context of the one of largest arbitration systems, the No Surprises Act, a 2022 federal law which resolves payment disputes between insurers and providers for surprise, out-of-network medical bills. We estimate a structural model of arbitrator preferences using public data from hundreds of thousands of disputes and provide economic interpretations of behavior in arbitration. Finally, we evaluate how the design of the arbitration system impacts important outcomes in the employer-sponsored health insurance market, namely negotiated rates and health plan network structure. (Joint with Christopher Whaley)