We present a method for arbitration between human and robot involvement in a collaborative physical task execution based on ergonomic metrics. The existing methods for ergonomic control of physical human-robot collaboration perform the real-Time arbitration primarily based on a single type of ergonomic metric. The novelty of our approach is twofold. First, the system enables real-Time arbitration based on combining two types of ergonomic metrics: preventive and reactive. Second, we use a preventive metric to prevent worker fatigue and discomfort due to overexertion in the future and a reactive metric to avoid immediate fatigue and discomfort. To this end, we considered two metrics respectively: human arm manipulability and muscle fatigue. The developed multi-metric arbitration method translates the human multi-metric state to a robot control level over a collaborative task execution using a finite state machine. We demonstrate the proposed method on a Kuka LWR iiwa robotic arm in a collaborative human-robot polishing task that requires a specific force production.