When AI counts research grants, human disagreement can outweigh sampling error

The study examines 121,070 distinct grant-purpose texts appearing across 799,675 US tax-filing records for grants to colleges and universities in 2020–2024. Those records represent $126.4 billion in paid or committed amounts. The main estimate concerns a narrower $102.2 billion domain: paid grants, with research-capital rows excluded. Crucially, the study counts reported dollars whose stated purpose qualifies as research under a codebook—not how much money institutions actually spent on research.

Repeated wording makes the classification problem unusual. One purpose text can appear on thousands of grants, so a single reading affects every record sharing that text. One text in the dataset covers 45,082 rows and $13.9 billion. Consequently, ordinary classification accuracy is not the main objective: a mistake attached to substantial funding can matter more than many mistakes on small grants.

Koomullil compares a rule-based classifier with three language models. Three people independently classified a probability sample of 651 texts under the same codebook, without seeing machine outputs or one another’s answers. Sampling favoured larger monetary amounts within groups defined by the language models’ voting patterns, while some texts were included with certainty. The analysis therefore accounts for unequal chances of selection rather than treating the human sample as a simple random collection.

To improve the predictions, the study fits a statistical calibrator using machine outputs and text features. It then estimates totals by combining predictions across the full dataset with a weighted correction for the errors observed in the human sample. The intuition is straightforward: AI supplies a preliminary count, while sampled human readings estimate how that count should be adjusted. Cross-fitting keeps each sampled text’s own label out of the model predicting it.

Eight predictors initially produce totals ranging from $11.2 billion to $15.0 billion. After correction against the first human reader, their estimates fall within roughly $0.4 billion of one another. The calibrated panel gives $11.29 billion, with a 95% sampling interval of approximately $10.4 billion to $12.1 billion. Tuning how strongly predictions influence the estimate narrows the interval by about 8% relative to the human-sample estimator alone. The improvement is modest partly because grouping the sample by machine votes already captures much of the models’ information.

These results have qualified statistical foundations. For predictions fixed independently of the sample, the underlying weighted difference estimator is exactly unbiased. Related exact results hold for the specified cross-fitting construction under independent, Poisson sampling. The actual fixed-size sampling procedure and reported ratio-based estimates require approximations. Simulations that refit the calibrator generally support the procedure, but one synthetic scenario produces coverage below the nominal 95% level. Agreement between corrected totals is therefore not a universal guarantee of reliable intervals.

The paper also asks which texts humans should review next. In a replay where every purchased label counts against the budget, a two-phase strategy first samples by monetary mass, trains its calibrator, then targets additional review using both monetary importance and predicted uncertainty. With 100 texts available, allocating a quarter to the first phase reduces root-mean-square estimation error by 28% against dollar-proportional sampling without a model. These are replays on a weighted pool built from the existing human sample, not a prospective deployment. With an overconfident, uncalibrated predictor, uncertainty-targeted review performs worse; mixing it with ordinary random sampling reduces that vulnerability.

Another experiment accepts confident machine labels while targeting a specified share of mislabelled dollars. One rule accepts about 80% of unsampled dollars at a 5% target, with approximately 0.3% error in nested held-out evaluation. However, its unequal-weight statistical bound lacks a finite-sample justification. Favourable stress tests do not establish deployment guarantees. Treating accepted labels as exact can also invalidate an interval for the combined total.

The largest unresolved uncertainty is human interpretation. The three readers agree on research-or-not for 77% of sampled texts, representing 91% of weighted dollars. Yet their corrected totals differ by $3.93 billion—about 2.2 times the first reader’s sampling-interval width. No adjudication establishes which reading is right. Institution-level intervals also perform poorly in simulations, and the full commercial dataset is unavailable publicly. The preprint’s central distinction is that statistical correction can reduce machine-dependent differences without resolving what the underlying human labels should mean.