LLM-as-a-judge approaches are a practical and effective way of assessing a range of text tasks. However, when using pairwise comparisons to rank a set of candidates, the computational cost scales quadratically with the number of candidates, which has practical limitations. This paper introduces a Product of Expert (PoE) framework for efficient LLM Comparative Assessment. Here individual comparisons are considered experts that provide information on a pair's score difference. The PoE framework combines the information from these experts to yield an expression that can be maximized with respect to the underlying set of candidates, and is highly flexible where any form of expert can be assumed. When Gaussian experts are used one can derive simple closed-form solutions for the optimal candidate ranking, and expressions for selecting which comparisons should be made to maximize the probability of this ranking. Our approach enables efficient comparative assessment, where by using only a small subset of the possible comparisons, one can generate score predictions that correlate well with human judgements. We evaluate the approach on multiple NLG tasks and demonstrate that our framework can yield considerable computational savings when performing pairwise comparative assessment. With many candidate texts, using as few as 2% of comparisons the PoE solution can achieve similar performance to when all comparisons are used.

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