In social robot navigation, traditional metrics like proxemics and behavior naturalness emphasize human comfort and adherence to social norms but often fail to capture an agent's autonomy and adaptability in dynamic environments. This paper introduces human empowerment, an information-theoretic concept that measures a human's ability to influence their future states and observe those changes, as a complementary metric for evaluating social compliance. This metric reveals how robot navigation policies can indirectly impact human empowerment. We present a framework that integrates human empowerment into the evaluation of social performance in navigation tasks. Through numerical simulations, we demonstrate that human empowerment as a metric not only aligns with intuitive social behavior, but also shows statistically significant differences across various robot navigation policies. These results provide a deeper understanding of how different policies affect social compliance, highlighting the potential of human empowerment as a complementary metric for future research in social navigation.