Our findings stress the importance of leveraging the distributional output of LLM-as-a-judge, as opposed to using the text interface alone.

Check out the full paper at arxiv.org/pdf/2503.03064!

For listwise ranking, although the mean does not improve accuracy, it drastically improves calibration. We also find that accuracy is maximized by directly predicting the list without an intermediate pairwise step, further underscoring the limitations of CoT for judgment.

For pairwise ranking, we compare pre- vs. post-aggregation (bottom vs. top in figure) of the two presentation orders' judgments. Small judges suffer from severe position bias, but pre-aggregation leverages the relative magnitudes of preference, boosting accuracy by 56.7→73.1.

We further explore novel methods of comparing score distributions.

1. The mode loses even to other discrete methods such as the median or first percentile (and the gap grows when we use finer judgment granularity).

2. Incorporating risk aversion often improves performance.

2. Chain-of-thought prompting leads to sharp judgment distributions. Removing it increases the spread of the distribution, often improving performance, and more so for the mean than for the mode, revealing the synergy between eliciting and using distributional judgment.

1. Taking the mean of the judgment distribution consistently outperforms taking the mode, across the pointwise, pairwise, and listwise settings.