Algorithmically Establishing Trust in Evaluators

An evaluator, such as an LLM-as-a-judge, is trustworthy when there exists some agreed-upon way to measure its performance as a labeller. Traditional approaches either rely on testing the evaluator against references or assume that it knows' somehow the correct labelling. Both approaches fail when references are unavailable: the former requires data, and the latter is an assumption, not evidence. To address this, we introduce the No-Data Algorithm’, which provably establishes trust in an evaluator without requiring any labelled data. Our algorithm works by successively posing challenges to said evaluator. We prove that after $r$ challenge rounds, it accepts an evaluator which knows the correct labels with probability $ \geq 1 - (1/4)^r$, and reliably flags untrustworthy ones. We present formal proofs of correctness, empirical tests, and applications to assessing trust in LLMs-as-judges for low-resource language labelling. Our work enables scientifically-grounded evaluator trust in low-data domains, addressing a critical bottleneck for scalable, trustworthy LLM deployment.

💡 Research Summary

The paper tackles a fundamental problem in modern AI evaluation: how to assess the trustworthiness of an evaluator (such as an LLM‑as‑judge) when no labeled data are available. Traditional approaches either require a reference dataset for testing or assume the evaluator already knows the correct labels. Both strategies break down in low‑resource settings where annotations are scarce, expensive, or benchmarks are contaminated.

To fill this gap, the authors introduce the “No‑Data Algorithm,” a protocol that can certify an evaluator’s reliability without any ground‑truth labels. The algorithm consists of two players—a verifier (V) and an evaluator (E)—who engage in a multi‑round interactive game called the Evaluator‑Verifier (EV) protocol. For each unlabeled instance x, the evaluator first proposes a label y = E(x). Then, over r rounds, the evaluator must generate a “similar” instance x′ together with a partial label ˜y′. The verifier randomly selects one of two challenges:

1. Permutation Equality (Challenge 1) – V checks whether the internal structure of x′ matches that of x with respect to a known rubric C. Concretely, for every sub‑component s of x there must exist a counterpart t in x′ such that all criteria c∈C evaluate identically on s and t.

2. Isomorphism Equality (Challenge 2) – V checks whether the overall rubric evaluation vectors are identical, i.e., C(x′) = C(x).

If the evaluator fails either challenge, the round ends in failure; otherwise the round repeats. Because the challenges are mutually exclusive and together capture both structural and functional aspects of the labeling function, an evaluator that truly knows the underlying labeling map f (assumed to be a composition f = σ∘C of a rubric C and an aggregator σ) will pass every round with certainty. A dishonest evaluator can only hope to pass by luck, and the probability of escaping detection in a single round is 1/4. Consequently, after r rounds the failure probability drops to (1/4)^r (Lemma 5.1).

The No‑Data Algorithm then uses the outcome of the EV protocol to decide whether to keep the original label or to flip it with a user‑specified probability ϕ. Theorem 5.2 links the evaluator’s intrinsic accuracy α, the flip probability ϕ, and the number of rounds r to the expected overall accuracy of the algorithm:

E