The LLM-as-a-judge (LLMaJ) framework offers a cost-effective and reproducible solution for automatic evaluation. However, current evaluation practices typically compare LLMaJ judgments against aggregated ground-truth labels, overlooking the valuable information contained in Human Label Variation (HLV). Inspired by an increasing line of work that proposes to leverage HLV, we systematically study LLMaJ performance on predicting both a single, aggregated ground truth hard-label and unaggregated soft-labels that represent Human Judgment Distributions (HJD). Our results across five diverse datasets reveal that while LLMs achieve near human-level performance at hard-label prediction on most tasks, they exhibit poor performance when predicting soft-labels. To address this limitation, we propose NAPHA (eNtropy-Aware Post-Hoc Alignment), a simple yet effective lightweight post-hoc alignment method that matches the LLM distribution to the HJD by first assigning an instance to a discrete entropy class and then routing it to specialized, trained alignment models. We find that NAPHA consistently improves soft-labels prediction across base LLM models and datasets, with particularly strong gains on high-entropy instances where capturing diverse human perspectives is most critical. We also show via oracle experiments that improving entropy class prediction can substantially enhance NAPHA's practical effectiveness.

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