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How to Stress-Test LLM Judges Fairly

A Fixed-Budget, Cluster-Aware Standard for LLM-as-a-Judge Evaluation: A Multi-Hop RAG Stress Test | alphaXiv []( []( []( []( []( []( We're hiring Paper 4 / 11 Hide Tools ⌘ / Open Tools A Fixed-Budget, Cluster-Aware Standard for LLM-as-a-Judge Evaluation: A Multi-Hop RAG Stress Test A Fixed-Budget, Cluster-Aware Standard for LLM-as-a-Judge Evaluation: A Multi-Hop RAG Stress Test Camilo Chacón Sartori*José H. García Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, Barcelona, Spain @ @ Code and materials: *Corresponding author Abstract Retrieval-augmented generation (RAG) sys- tems are often compared by asking a large lan- guage model (LLM) judge which answer is better. For multi-hop RAG, this has become a measurement problem as much as a modeling problem: the same score can reflect retrieval

quality, answer length, lexical overlap, or a sta- tistical test that ignores clustered data. We ask what happens when these choices are made ex- plicit. We propose a minimum measurement stan- dard for LLM-as-a-judge comparisons in RAG. The standard fixes the top-100 candidate pool, evidence budget, answer cap, generator, and prompt; it also requires pre-registered hypothe- ses, cluster-aware inference, an exact clus- ter sign-flip check when feasible, and second- judge replication. Clustered benchmarks can overstate progress; the field should adopt this standard. We stress-test it with Genetic Algo- rithm Decoder for Multi-hop Evidence Compo- sition (GADMEC), an evolutionary evidence selector, on 400 multi-hop questions in com- puter science/machine learning (CS/ML) and Materials Science. The protocol changes the empirical story.A binomial test makes all four semantic-baseline comparisons look sig- nificant; cluster-aware inference leaves only one Bonferroni-significant result. BM25 beats pure semantic GADMEC under the same bud- get, while a lexical-semantic hybrid recovers in CS/ML and narrows the Materials Science gap. 1 Introduction RAG systems are increasingly compared with pair- wise LLM-as-a-judge protocols: two answers are shown to a judge model, and the preferred answer is counted as a protocol is attractive because it is simple and cheap to also hides important choices. A method can look bet- ter because it selected better evidence, because it induced longer answers, because it matched lexi- cal cues that dense retrieval missed, or because the statistical test treated clustered examples as inde- pendent. In multi-hop RAG, these mechanisms are easy to mix. This paper asks whether the headline of a RAG comparison survives when those choices are con- trolled. In our experiment, the answer is mixed. A binomial test would make all four pre-registered semantic-baseline comparisons look significant. Cluster-aware inference leaves only one compar- ison significant after Bonferroni correction, with two more significant only before correction. The empirical story therefore depends not only on the selector, but also on the measurement protocol used to evaluate it. We make two claims. First, pairwise LLM-as-a- judge evaluation for multi-hop RAG is more fragile than standard reporting suggests. Second, the field should adopt a minimum measurement standard for cluster-structured LLM-as-a-judge benchmarks. The standard fixes evidence and answer budgets. It separates confirmatory from exploratory analy- ses through pre-registration and a public deviation log, uses cluster-aware inference, adds an exact sign-flip check when the cluster count permits it, and replicates headline results with a second judge. These components are not individually new. The contribution is to make them operate together in one controlled RAG comparison and show how the conclusions change. We stress-test the standard with Genetic Al- gorithm Decoder for Multi-hop Evidence Com- position (GADMEC), a Biased Random-Key Ge- 1 arXiv:2605.27789v1 [ ] 27 May 2026 []( " " "mailto: @ ")[](mailto: @ "mailto: @ ")[]( " " netic Algorithm (BRKGA; Gonçalves and Resende, 2011) for evidence subset selection. GADMEC is the instrument, not the protagonist. Its evolu- tionary search is separated from the decoder that enforces budget and diversity constraints, so a random-fitness ablation can test whether the fitness function contributes beyond the decoder machin- ery. Contributions. 1.

A fixed-budget evaluation design for LLM- as-a-judge comparisons in RAG: same top- 100 candidate pool, 2000-token evidence bud- get, 300-token answer cap, and generator set- tings for all methods. 2. A pre-registered analysis protocol:four Bonferroni-corrected primary hypotheses, an addendum for length matching and ablations, and a deviation log for post-hoc analyses. 3. A cross-domain benchmark: 687 arXiv pa- pers (2024–2026), a 3-level taxonomy, 10 cross-subfield combinations per area, 20 ques- tions per combination, and 200 contrastive multi-hop questions per area. 4. A methodological demonstration: the head- line of a multi-hop RAG comparison can change when inference respects the cluster binomial test would have reported all four primary tests as signifi- cant; wild-cluster bootstrap leaves only one Bonferroni-significant result. The same proto- col exposes a lexical-vs-semantic axis: BM25 beats pure semantic GADMEC, while a hy- brid recovers in CS/ML. The paper unfolds as follows. Section 2 situates fixed-budget evaluation relative to LLM-as-a-judge evaluation, multi-hop question answering (QA), subset selection, and pre-registration. Sections 3 and 4 define GADMEC, the baselines, and the controlled evaluation protocol. Section 5 reports the pre-registered results, length controls, content- distance diagnostics, and ablations. Sections 6–8 interpret the mechanisms, conclude, and state the limitations. 2 Related Work LLM-as-a-Judge Evaluation for RAG. Reference-free LLM-as-a-judge evaluation is now common in RAG formalised the setup for retrieval-augmented generation (Es et al., 2024), and recent surveys catalogue its variants (Li et al., 2025). The closest concern for this paper is length bias (Zheng et al., 2023; Dubois et al., 2024). We control both input and output budgets, then ask what signal remains after length matching. Multi-hop QA , 2Wiki- MultiHop, MuSiQue, and GRADE target chained- evidence multi-hop reasoning (Lee et al., 2025). Our questions have a different shape:contrastive composition(“how do X and Y differ on as- pect Z”). This makes evidence selection budget- sensitive because a good answer must cover several sub-aspects at once. Combinatorial subset selection in retrieval. Maximal Marginal Relevance (MMR; Carbonell and Goldstein, 1998) and Determinantal Point Pro- cesses (DPPs; Kulesza and Taskar, 2012) are clas- sical instances. Genetic algorithms have been ap- plied to RAG primarily for adversarial attack and corpus poisoning (Cho et al., 2024).We use a BRKGA constructively: the candidate pool is the search space, and the selected subset is the evidence plan. Pre-registration in -registration is rare in natural language processing (NLP). We follow social-science practice with a primary registration, timestamped addenda, and a deviation log separat- ing confirmatory and exploratory analyses. Together, these strands motivate an evaluation instrument rather than only a new retriever. The selector is allowed to vary; the evidence budget, answer cap, judge protocol, and evidential status of each analysis are not. 3 Method We first define the selector, then the controls that make the comparisons interpretable. Figure 1 sum- marizes the full pipeline. The key rule is simple: every method sees the same candidates and uses the same generation settings. Only the evidence plan changes. 3.1 GADMEC fitness GADMEC’s fitness over a candidate evidence plan P combines five components: f(P) =α COV+β DIV+γ COST+δ COH+ε SUB 2

[]( "Gonçalves and Resende")[]( "2011")[]( "Es et al.")[]( "2024")[]( "Li et al.")[]( "2025")[]( "Zheng et al.")[]( "2023")[]( "Dubois et al.")[]( "2024")[]( "Lee et al.")[]( "2025")[]( "Carbonell")[]( "and Goldstein")[]( "1998")[]( "Kulesza and Taskar")[]( "2012")[]( "Cho et al.")[]( "2024")[]( "Figure 1") 1. Corpus construction Taxonomy 3 levels 2 areas×8 subareas×5 topics arXiv search per combo 700 candidate combos 10 approved combos / area 5 TOP + 5 NICHO 687 papers chunked + embedded 2. Question generation Contrastive prompt “How do X and Y differ in. . . ” Sample 3 papers / combo ×2 paper triplets GPT-5.4-mini T= 0.7 200 questions / area multi-hop, no method names 3. Evaluation Retrieval top-100 chunks by cosine 4 evidence plans GADMEC / Greedy / MMR / BM25 GPT-5.4-mini answers T= 0, seed=42 Opus 4.7 judge (API) randomized A/B positions Figure 1: GADMEC pipeline. The protocol first builds a taxonomy-filtered corpus, then generates contrastive multi-hop questions, and finally evaluates four selectors under the same candidate pool, evidence budget, generator, answer cap, and judge (Claude Opus 4.7, randomised answer-A/answer-B positions). The only intended source of variation is the evidence selector. We re-judge the six headline comparisons with a second strong proprietary judge from a different provider (DeepSeek V4 Pro, thinking mode) to assess inter-judge robustness (§5.5). Here COV rewards mean query similarity, and DIV rewards pairwise dissimilarity among selected is a normalised token penalty,COH is centroid–query similarity, and SUB measures cover- age of GPT-5.4-mini query sub-aspects embedded with all-MiniLM-L6-v2. We use α= 0.30, β= 0.15, γ= 0.00, δ= 0.15, ε= 0.40, with sub-coverage threshold 0.40. The BM25 lexical component ζ is 0 for pure se- mantic GADMEC and activated only in the hybrid analyses. 3.2 BRKGA decoder BRKGA (Gonçalves and Resende, 2011) repre- sents each plan as random keys in[0,1]n and leaves feasibility to a decoder. The decoder sorts chunks by key and accepts them greedily until the plan reaches the 2000-token budget. It also enforces minimum query similarity 0.15, redundancy thresh- old 0.80, and at least three k-means thematic clus- search uses population size 20, elite fraction 0.24, elite-inheritance probability 0.70, at most 50 generations, early stopping after 15 stag- nant generations, and seed 42. 3.3 Baselines We compare against greedy top-k budget-fill, Max- imal Marginal Relevance (MMR) with λ= 0.5 (Carbonell and Goldstein, 1998), and the BM25 lexical retriever (k 1= 1.5, b= 0.75). All meth- ods operate on the same top-100 cosine-pre-filtered candidate pool. Win-rate differences therefore re- flect how methods choose evidence from the same pool, not whether one method had access to better candidates. 3.4 Question generation and judging Question generation uses a contrastive multi-hop prompt with GPT-5.4-mini at T= area has 10 combinations,with 20 questions per use GPT-5.4-mini at T= 0, seed 42, evidence-only prompting, and max_completion_tokens=300. Claude Opus 4.7 judges randomised answer-A/answer-B pairs in a single pass using a fixed pairwise prompt asks for a global preference based on factual correctness, completeness, evidence sup- port, clarity, specificity of evidence-backed claims, multi-source synthesis, and coverage of the ques- tion are allowed but reserved for answers that are truly equivalent; ties are recorded and excluded from the win-rate denominator. 4 Experimental Setup