A fail-operational system for highly automated driving must complete the driving task even in the presence of a failure. This requires redundant architectures and a mechanism to reconfigure the system in case of a failure. Therefore, an arbitration logic is used. For functional safety, the switch-over to a fall-back level must be conducted in the presence of any electric and electronic failure. To provide evidence for a safety argumentation in compliance with ISO 26262, verification of the arbitration logic is necessary. The verification process provides confirmation of the correct failure reactions and that no unintended system states are attainable. Conventional safety analyses, such as the failure mode and effect analysis, have its limits in this regard. We present an analytical approach based on formal verification, in particular model checking, to verify the fail-operational behaviour of a driving system. For that reason, we model the system behaviour and the relevant architecture and formally specify the safety requirements. The scope of the analysis is defined according to the requirements of ISO 26262. We verify a fail-operational arbitration logic for highly automated driving in compliance with the industry standard. Our results show that formal methods for safety evaluation in automotive fail-operational driving systems can be successfully applied. We were able to detect failures, which would have been overlooked by other analyses and thus contribute to the development of safety critical functions.