Are explainable AI (XAI) evaluation strategies aligned? Comparing subjective, objective, and mathematical evaluation measures using saliency maps

The evaluation of explainable AI (XAI) approaches often relies on three families of methods: subjective measures (e.g., questionnaires on trust or satisfaction), objective measures (e.g., task performance metrics), and mathematical metrics (e.g., for faithfulness). Yet, it remains unclear how these families align or diverge in practice. In a{preregistered} between-subjects study (N=166), we use three established saliency map techniques (LIME, Grad-CAM, Guided Backpropagation) as a testbed to examine this issue. We find that each family of methods leads to different conclusions: participants reported no differences in trust or satisfaction, Grad-CAM improved user performance, while mathematical metrics favored Guided Backpropagation. At the same time, mathematical metrics were only partially related to user performance, and these relationships were sometimes counterintuitive. Our findings highlight the methodological importance of comparing subjective, objective, and mathematical approaches when evaluating XAI, illustrating both tensions and aspects that are aligned. We discuss implications for XAI evaluation frameworks.