Beyond correlation: The impact of human uncertainty in measuring the effectiveness of automatic evaluation and LLM-as-a-judge

The effectiveness of automatic evaluation of generative models is typically measured by comparing it to human evaluation using correlation metrics. However, metrics like Krippendorff's $\alpha$ and Randolph's $\kappa$, originally designed to measure the reliability of human labeling, make assumptions about human behavior and the labeling process. In this paper, we show how *relying on a single aggregate correlation score* can obscure fundamental differences between human behavior and automatic evaluation methods, including LLM-as-a-Judge. Specifically, we demonstrate that when the proportion of samples with variation or uncertainty in human labels (gathered during human evaluation) is relatively high, machine labels (generated by automatic evaluation methods) may superficially appear to have similar or better correlation with the human majority label compared to human-to-human (HH) correlation. This can create the misleading impression that automatic evaluation is accurate enough to approximate the human majority label. However, as the proportion of samples with consistent human labels increases, the correlation between machine labels and human majority labels declines, falling below HH correlation. Based on these findings, we first propose stratifying results by human label uncertainty to provide a more robust analysis of automatic evaluation performance. Second, recognizing that uncertainty and variation are inherent in perception-based human evaluations, such as those involving attitudes or preferences, we introduce a new metric - *binned Jensen-Shannon Divergence for perception* for such scenarios to better measure the effectiveness of automatic evaluations. Third, we present visualization techniques -- *perception charts*, to compare the strengths and limitations of automatic evaluation and to contextualize correlation measures appropriately