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From Self-Confidence to Statistical Accuracy: Scaling Human-in-the-Loop Evaluation with Direct and LLM-Assisted Auditing

Harine Choi, Chenchen Kuai, Zihao Li, Jiwan Jiang, Yunlong Zhang, Zhiwen Fan, Zhengzhong Tu, Yang Zhou

arXiv:2610.35698v1cs.CL

TL;DR

Large-scale LLM and MLLM evaluation cannot always rely on exhaustive human verification, while confidence and automated judges are imperfect signals. The paper develops a statistical framework for confidence-stratified auditing and judge-assisted estimation, then compares their label and cost efficiency. Across the studied benchmarks, miscalibrated confidence remains useful for stratified auditing, but judge-assisted savings depend on calibration and inference costs.

  • Problem

    Exhaustive human verification is impractical at scale, and miscalibrated confidence or imperfect judges complicate recovering population accuracy from partially verified outputs.

    Source: §1 · p. 1

  • Method

    The paper unifies confidence-stratified direct auditing and sensitivity/false-positive-rate-corrected judge evaluation, deriving uncertainty and human-label and cost-efficiency boundaries.

    Source: §1 · pp. 1–2

  • Results

    Across MMLU-Pro and MMMU-Pro, miscalibrated self-reported confidence supported stratified auditing with low bias; at 200 labels, RMSE fell from 4.56 percentage points under uniform allocation to 2.46 under proportional allocation.

    Source: §4.3 · p. 6, §5 · pp. 7–8

  • Takeaways & Limitations

    Confidence-guided auditing can recover population accuracy without calibrated confidence, while judge-assisted efficiency depends on discrimination, calibration uncertainty, and inference cost.

    Source: §1 · p. 2, §5 · p. 8

    The study uses multiple-choice benchmarks with known references and simulated partial auditing, assumes representative sampling and stable verifier behavior, and treats cost boundaries as analytical guidance rather than universal guarantees.

    Source: Limitations · p. 8

Abstract

from arXiv · show

For large language models (LLMs) and multimodal large language models (MLLMs), model-reported self-confidence is often miscalibrated, yet it may still be useful for efficient evaluation. At the same time, LLM-as-a-judge offers a scalable alternative to direct human auditing, but its practical benefit depends on calibration quality and inference cost. This paper develops a unified statistical framework for both evaluation routes under alternative sampling strategies. For direct auditing, confidence-stratified sampling is used to recover population accuracy from partially verified outputs without requiring calibrated confidence. Finite-sample uncertainty is characterized, and the analysis shows how highly uneven confidence strata affect audit efficiency and label allocation. For judge-assisted evaluation, the judge is modeled through sensitivity and false-positive rate, yielding an error-corrected estimator with calibration uncertainty. The two routes are then compared through human-label and total-cost efficiency boundaries. Experiments on MMLU-Pro and MMMU-Pro show that miscalibrated self-confidence can still support statistically valid stratified auditing. Under highly imbalanced confidence distributions, proportional allocation substantially reduces estimation error relative to equal-per-stratum allocation. For judge-assisted evaluation, only a small subset of target--verifier pairs satisfies the idealized human-label efficiency condition, and automated inference costs can further limit potential savings. These findings clarify the statistical and economic conditions under which confidence-guided auditing and automated verification are useful.

1 Introduction

Large-scale LLM and MLLM evaluation makes exhaustive human verification impractical, while partial verification requires statistically valid population-accuracy estimates. The paper unifies confidence-guided direct auditing and judge-assisted evaluation, comparing their precision and cost conditions.

1 Introduction

  • Exhaustive human verification is impractical at scale, and reliable reference labels can account for a substantial share of evaluation cost.Partial verification therefore makes population accuracy and uncertainty an inference problem.Source: §1 · p. 1
  • Miscalibrated confidence can still guide auditing, but low-confidence-only review may underrepresent errors among confident predictions.Confidence strata can differ substantially in size, making allocation important for estimation precision.Source: §1 · p. 1
  • Judge-assisted evaluation still requires human labels to estimate and correct judge error rates, while calibration uncertainty carries into the accuracy estimate.Its relative efficiency also depends on judge discrimination and automated-inference and human-review costs.Source: §1 · p. 1
  • The framework treats confidence as a stratification variable, not a trusted correctness probability, and models judge-assisted evaluation through sensitivity and false-positive rate.Both routes include finite-sample uncertainty and are compared through human-label and cost-efficiency boundaries.Source: §1 · pp. 1–2

2 Related Work

Related work covers uncertainty-guided review, label-efficient statistical evaluation, and LLM-based judging. This paper focuses on confidence-stratified auditing and compares it with calibrated judge-assisted estimation at a common target precision.

2 Related Work

  • Confidence-guided population evaluation creates verification bias because it determines which correctness labels become observable, requiring explicit accounting for sampling.This differs from selective prediction's coverage–error-control trade-off.Source: §2 · p. 2
  • Prior label-efficient methods use adaptive sampling, learned surrogates, prediction-based correction, and stratified allocation to improve evaluation from limited labels.Prediction-weight estimation can itself be uncertain with few labels, so savings depend on budget and auxiliary-signal usefulness.Source: §2 · p. 2
  • LLM judges can exhibit position, self-preference, knowledge, and format biases; this work treats binary judging as imperfect screening and compares calibrated judging with direct auditing.The comparison uses a common target precision and derives human-label and total-cost efficiency boundaries.Source: §2 · p. 2

3 Statistical Framework and Derivations

The framework estimates population accuracy from partial verification using confidence strata and characterizes precision under fixed allocations. It also models judge-assisted estimation and derives human-label and total-cost conditions for comparing it with direct auditing.

3.1 Population Accuracy and Identification

  • Confidence-stratified estimation weights audited stratum accuracy by each stratum's population share, and does not require calibrated confidence.Random sampling within strata and population weighting provide statistical validity; confidence is useful when it separates outputs with different correctness rates.Source: §3.1 · pp. 2–3
  • Identification bounds describe population accuracies compatible with observed labels, whereas the sampling design supplies probabilistic guarantees on estimation error.Observed labels alone do not determine every unaudited outcome.Source: §3.1 · p. 3

3.2 Finite-Sample Accuracy and Audit Precision

  • Precision depends on stratum weights, within-stratum variability, and audit allocation; the Hoeffding bound is conservative because it omits finite-population corrections.Ignoring integer and capacity constraints, proportional allocation minimizes the Hoeffding denominator, while Neyman allocation minimizes estimator variance.Source: §3.2 · pp. 3–4

3.3 Accuracy Recovery with an LLM Judge

  • Judge-assisted recovery maps the judge's acceptance rate to target accuracy using sensitivity and false-positive rate, requiring a nonzero discrimination gap.High overall judgment accuracy alone does not ensure strong discrimination; calibration examples are assumed representative within correctness classes.Source: §3.3 · p. 4
  • Increasing automated judgments reduces acceptance-rate uncertainty but cannot remove calibration uncertainty, and a small discrimination gap amplifies all three variance contributions.The variance also includes uncertainty from human calibration of sensitivity and false-positive rate.Source: §3.3 · p. 4

3.4 Human-Label Budget and Label Efficiency

  • The human-label efficiency ratio is idealized: a value above 1 favors verifier calibration only when automated-sampling uncertainty is negligible.For finite automated sample size, the additional Dv/M variance contribution reduces that advantage; the reference comparison is direct random auditing.Source: §3.4 · pp. 4–5

3.5 Cost-Efficiency Boundary

  • Judge-assisted evaluation is less expensive only when its cost-efficiency condition holds, accounting for both calibration uncertainty and automated-evaluation cost.As automated cost relative to human-label cost approaches zero, the boundary reduces to the human-label efficiency condition.Source: §3.5 · p. 5

4 Experiments and Results

Across MMLU-Pro and MMMU-Pro, self-confidence tracks accuracy but is miscalibrated; confidence-stratified audits recover population accuracy, while judge-assisted efficiency depends on verifier discrimination and inference cost.

4.1 Experimental Setup

  • The evaluation uses 8,000 MMLU-Pro questions and a fixed 1,000-question MMMU-Pro subset; audits simulate partial verification, and each of eight models is compared with seven verifiers.The cost estimates use observed verifier tokens and October 10, 2026 API prices, excluding answer-generation costs, retries, discounts, taxes, and surcharges.Source: §4.1 · p. 5

4.2 Self-Confidence Is Informative but Miscalibrated Across Benchmarks

  • On MMLU-Pro and MMMU-Pro, confidence generally tracks accuracy but is not calibrated; on MMMU-Pro all eight models are overconfident, with gaps reaching 59.6 points.Even Claude Sonnet 5 has a 10.1-point confidence–accuracy gap and an ECE of 0.108 on MMMU-Pro.Source: §4.2 · p. 6

4.3 Partial Audits Reliably Recover Population Accuracy

  • At 200 labels, MMLU-Pro RMSE falls from 4.56 percentage points under uniform allocation to 2.46 under proportional allocation; observed failure probabilities remain below Hoeffding bounds.Confidence-stratified auditing recovers GPT-5.5’s MMLU-Pro accuracy of 80.54%; MMMU-Pro shows the same overall pattern, with greater variability at small budgets.Source: §4.3 · p. 6, Figure 3 · p. 7

4.4 Verifier Efficiency across Benchmarks

  • Only 6 of 56 MMLU-Pro target–verifier pairs exceed the human-label efficiency threshold, and no MMMU-Pro pair does; GPT-5.5 verifying Llama-3.1-8B has 0.89 judgment accuracy and the highest efficiency ratio, 1.45.The most favorable cost break-even threshold for that pair is approximately $0.09; inference cost can limit savings, and cheaper inference cannot remove the calibration floor.Source: §4.4 · p. 7

5 Conclusion

The paper presents a unified framework for estimating LLM and MLLM accuracy under limited human verification. Its conclusion is that miscalibrated confidence can still support low-bias stratified auditing, while judge-assisted evaluation depends on discrimination, calibration uncertainty, and inference cost.

5 Conclusion

  • Across MMLU-Pro and MMMU-Pro, miscalibrated self-confidence remained useful for stratified auditing that recovered population accuracy with low bias.Source: §5 · p. 8
  • The framework models LLM verification through sensitivity and false-positive rate, rather than relying on judgment accuracy alone.Source: §5 · p. 8
  • Verifier benefits depend on discrimination, calibration uncertainty, and inference cost; high judgment accuracy alone does not guarantee efficient auditing.Source: §5 · p. 8

Limitations

The study’s conclusions are bounded by its multiple-choice benchmark setting, simulated audits, and assumptions about sampling and verifier behavior.

Limitations

  • The analysis covers multiple-choice LLM/MLLM benchmarks with known references and simulated partial auditing.Source: Limitations · p. 8
  • It assumes representative sampling and stable verifier behavior; human-label noise, distribution shift, open-ended evaluation, and continuous verifier confidence are not fully modeled.Source: Limitations · p. 8
  • Cost boundaries use observed token use and current API-price proxies, so actual costs may vary and the boundaries are analytical guidance, not universal deployment guarantees.Source: Limitations · p. 8

A Derivation of the Cost-Efficiency Boundary

The appendix derives when verifier-assisted evaluation can reduce total cost while meeting a target variance, accounting for both human calibration labels and automated judgments. The resulting boundary separates conditions favoring verifier assistance from those where it cannot be preferable under the stated criterion.

A Derivation of the Cost-Efficiency Boundary

B.1 Model Outputs and Calibration

The experimental appendices specify model outputs and benchmark populations, audit-allocation and simulation procedures, verifier judgments, and allocation constraints.

B.1 Model Outputs and Calibration

  • MMLU-Pro models returned an answer and a 1–100 correctness probability; calibration summaries use ten equal-width confidence bins and specified minimum bin counts.Source: §B.1 · p. 13

B.2 Fixed and Adaptive Audits

  • Audit simulations compare fixed and adaptive allocation strategies, using 5,000 independent replications per budget–allocation condition and reporting bias and RMSE.Source: §B.2 · p. 14

B.3 Verifier Judgments

  • Verifiers returned binary correctness judgments and estimated probabilities; the primary analysis uses binary judgments and computes rates separately for each target–verifier pair.Source: §B.3 · p. 14

C Audit Allocation Strategies

C.1 Fixed Audit Allocations

The section compares fixed and adaptive audit allocations, then extends confidence-stratified estimation to imperfect human labels and discusses the resulting uncertainty and identification limits.

C.1 Fixed Audit Allocations

  • Uniform allocation can oversample small confidence strata, while proportional allocation preserves their population representation and Neyman allocation favors prevalent, internally uncertain strata.Uniform allocation ignores stratum size and variability; Neyman allocation assigns fewer labels to strata whose accuracies are near zero or one.Source: §C.1 · pp. 14–15
  • Proportional allocation gives the strongest Hoeffding bound among these fixed stratified designs without requiring true stratum accuracies.Neyman allocation instead minimizes variance using within-stratum correctness variability, which must first be estimated.Source: §C.1 · p. 15, §C.2 · p. 15

C.2 Why Proportional and Neyman Allocation Differ

  • Proportional allocation minimizes a distribution-free concentration criterion, whereas Neyman allocation can reduce variance when stratum variability differs substantially.Neyman’s advantage depends on information that must first be estimated.Source: §C.2 · p. 15

C.3 Two-Stage Neyman Auditing

  • A two-stage Neyman design uses a small uniform pilot in each stratum to estimate variability and allocate the remaining audit budget.The pilot accuracy is stabilized so estimated variance does not become zero when all pilot labels agree.Source: §C.3 · pp. 15–16

C.4 Estimation after Adaptive Allocation

  • Because pilot outcomes determine later sample sizes, the estimator combines observed pilot totals with an expansion estimate for each stratum’s unaudited remainder.Conditioning on the pilot leaves the second-stage sample uniform over that remainder, preserving unbiasedness under population weighting.Source: §C.4 · p. 16

D.2 Confidence-Stratified Auditing with Imperfect Humans

D.3 Uncertainty in Human Reliability

  • When human reliability must be estimated, its uncertainty persists as audit budgets grow and can eventually limit population-evaluation precision.The uncertainty includes terms from estimating human reliability, beyond uncertainty from the audit sample.Source: §D.3 · p. 17

D.5 Practical Interpretation

  • Human error can distort judge calibration, and unknown human reliability generally leaves population accuracy unidentified from a single noisy label per output without additional assumptions or annotations.Adjudication, repeated annotation, or disagreement resolution can approximate the trusted reference process, with added costs.Source: §D.4 · p. 18, §D.5 · p. 18

E Additional Empirical Figures

The additional figures cover MMMU-Pro calibration, repeated-audit validation, and cross-model verification.

MMMU-Pro calibration

  • Figure 6 shows MMMU-Pro calibration through reliability curves, confidence-minus-accuracy by bin, ECE and Brier score, and accuracy versus mean confidence; seven runs contain 1,000 outputs and Sonnet 5 contains 998.Source: Figure 6 · p. 19

MMMU-Pro audits

  • Figure 7 presents MMMU-Pro audit results for GPT-5.5, based on 5,000 replications and four merged strata.Source: Figure 7 · p. 20

MMMU-Pro verification

  • No MMMU-Pro target–verifier pair has an idealized label-efficiency ratio above one, excluding self-verification.Source: Figure 8 · p. 21

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