Recovering LLM-Persona Accuracies from Unlabeled Votes

Algebraic (NTQR) evaluation infers how accurate a group of noisy classifiers was on a finite test using only their responses — no answer key. We test this end to end on real large language models. Three trader "personas" (optimistic, neutral, pessimistic), instantiated as system prompts, each make a binary bullish/bearish call on the same 64 market scenarios; we run the identical trio through six locally-hosted models via Ollama. For each model we recover per-persona, per-label accuracy with ErrorIndependentEvaluation (unsupervised) and score it against the authored ground truth (supervised), which is used only as a check. On the five models whose three judges all varied (mistral:latest, gemma4:latest, gemma3:4b, gemma2:2b, granite4.1:3b), the unsupervised algebra recovered persona accuracies to a mean absolute error of 0.012, within the 0.102 sampling-noise floor across all six per-label accuracy terms, with no labels -- including a persona's genuinely poor bullish accuracy of 0.57, recovered as 0.59. The other model collapsed at least one persona into a constant classifier (a judge that voted one way on all 64 scenarios), which makes the error-independent algebra unsolvable. The central, non-obvious result: inter-judge disagreement does not imply evaluability. Aggregate disagreement separated this run only because the unevaluable model(s) collapsed to 0.00; the five evaluable models spanned 0.03–0.23. What gates evaluation is a per-judge condition — every judge must vary (and answer) — not an ensemble one. We formalize this as a label-free evaluability diagnostic (a judge whose modal-vote fraction reaches 1.0 is a constant classifier; an unparseable vote is an abstention) that predicted exactly which models would be evaluable, before any solve and without ground truth. This is a concrete instance of the safety property the NTQR logic promises: it warns you when an ensemble is not good enough to be evaluated. A scenario bootstrap puts a 95% CI of [0.000, 0.038] on the recovery MAE (well inside the 0.102 noise floor), and a deterministic synthetic study generalizes the recovery beyond the finite set of real evaluable models — error falls like 1/√Q (slope -0.58, stable across ensembles) — while mapping two honest limits: the built-in failure alarm catches anti-correlated judges with no false positives yet can miss positively-correlated (shared-training) errors, and the two-solution tie-break inverts once judges are no longer clearly better than random — exactly where simple majority-voting evaluation, though biased, is the more robust fallback. --- Associated artifacts GitHub release: v1.0.0 (https://github.com/docxology/ntqr_llm/releases/tag/v1.0.0) DOI: https://doi.org/10.5281/zenodo.20498699 Zenodo: https://zenodo.org/records/20498699 PDF SHA-256: e1196698427f9fe04d1f3071705adb6e5459983649c78d7f5d074756e989148b