Metric-Dependent Annotation Saturation for Learning from Label Distributions

When annotators disagree on a label, the disagreement itself carries signal—and the number of annotators needed to capture it depends on the evaluation metric. We fine-tune NLI models on label distributions subsampled from ChaosNLI, a dataset providing 100 independent annotator judgments per item, and identify metric-dependent saturation. In our 3-class NLI setting, entropy correlation—whether the model identifies which items elicit disagreement—requires N ≈ 20–50 annotators to converge, while distributional match (KL divergence) saturates by N ≈ 10 (87–95% of improvement across five model seeds). This finding rests on a prior observation: soft labels carry item-specific signal that label smoothing cannot replicate. Across five smoothing intensities, entropy correlation clusters at r ≈ 0.45–0.49, while soft labels reach r = 0.643 (p < 0.001); per-item analysis traces this gap to smoothing’s inability to distinguish ambiguous items from clear ones. The soft-label advantage replicates across two architectures (DeBERTa, RoBERTa), a non-NLI-pretrained baseline, and an exploratory cross-domain evaluation on content safety. These results suggest that annotation budgets should be informed by the target evaluation metric rather than set uniformly.