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LLM Judge Validation Under Sparse Overlap: From Inference to Design

Sep 2026 · 0 citations · 36 references
Computer Science Mathematics

TL;DR

It is proved that overlap sparsity is the first-order determinant of wrong deployment decisions: at 5% pairwise overlap, wrong-decision rates reach 25% and the probability of selecting the wrong best judge among ten candidates is 65%.

Abstract

Validating an LLM-as-a-judge requires estimating its agreement with humans, yet annotation budgets rarely allow every item to be multiply labeled. We prove that this overlap sparsity is the first-order determinant of wrong deployment decisions: at 5% pairwise overlap, wrong-decision rates reach 25% and the probability of selecting the wrong best judge among ten candidates is 65%. The two actionable levers are overlap quantity and allocation. For quantity, we derive a minimum-overlap formula showing $\rho \geq 0.25$ suffices for non-borderline judges while borderline cases remain fundamentally hard. For allocation, a zero-cost stratified scheme halves false-rejection rates relative to random sampling when strata are informative. We validate on 10 LLM judges across four evaluation matrices spanning visual assessment, causal reasoning, and summarization.

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