Blind to the Pivotal Vote: Aggregate Independence Metrics Miss Where Verification Actually Helps

• URL: http://arxiv.org/abs/2608.06940v1
• Date: Fri, 07 Aug 2026 08:14:46 GMT
• Title: Blind to the Pivotal Vote: Aggregate Independence Metrics Miss Where Verification Actually Helps
• Abstract summary: We show that a majority-side replacement rule raises overall accuracy from 82.44% to 85.62% while invoking the signal on 16.2% of queries.<n>On HumanEval+/MBPP+, a majority-side replacement rule raises overall accuracy from 82.44% to 85.62% while invoking the signal on 16.2% of queries.
• Score: 9.710464466895521
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: LLM judge panels are a standard evaluation tool, but prior work reports highly correlated panel errors: nine judges provide roughly the effective information of two independent ones, and aggregation closes only a small fraction of the gap. A natural remedy--a signal from a different evidence source, e.g., executing a test suite--produced no distinguishable change in the panel's effective-vote count at scale (-0.04, 95\% CI [-0.10, +0.02]). Aggregate dependence and conditional decision utility are different questions. Elementary majority arithmetic fixes the affected set for single-ballot substitution: only decisions with a one-vote margin can change. The empirical question is whether panel error rates rise and useful substitutions concentrate there. They do: the entire accuracy gain concentrates on these pivotal queries, where it is large (+10.4 to +23.3 percentage points across three headline configurations), and is exactly zero elsewhere. We confirm the pattern across three code benchmarks and four panel sizes (a 9-judge extension and 56 dependent subsampling checks, gain +6.5 to +16.1 percentage points). On HumanEval+/MBPP+, a majority-side replacement rule raises overall accuracy from 82.44\% to 85.62\% while invoking the signal on 16.2\% of queries; signal-only remains stronger at 87.60\%. Thus population-level dependence diagnostics and margin-stratified utility are complementary, and the affected-set characterization yields a call-reduction rule for any specified single-ballot substitution policy.

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