Pairwise Comparison

Rank-based selection in dynamic environments acts on order information that becomes stale while it is being used. Tournaments, elitism, truncation, and Pareto selection may therefore consume rankings that no longer match the current fitness order, while full re-evaluation competes with search for the same budget. This paper formulates the missing information layer as a data-structure problem. A hidden total order on $n$ items drifts by adjacent transpositions, while a maintainer receives one truthful pairwise comparison per step and must answer rank queries continuously. We introduce the comparison patrol, a constant-time maintained-order structure using $3n+O(1)$ words, one comparison per update, deterministic verification-age bounds, and per-item displacement certificates. We prove lower bounds showing that oblivious and location-oblivious maintainers incur expected Kendall error $Ω(\min(α,1)n)$, and show that the patrol operates at the same order. A bump invariant yields exact self-stabilization after drift-free corruption: if the maximum rank overstatement is $L$, recovery takes at most $L$ aligned cycles and cannot finish before $L-1$. This gives a deterministic shock-recovery calculus and a crossover with full rebuild near $L\approx \log_2 n$. The maintained order is then transferred to evolving planar maxima and to evolutionary selection rules, giving deterministic bounds for truncation, tournament, elitist, and two-objective Pareto decisions under drifting fitness. Experiments up to $n=65{,}536$ audit the certificates, recovery laws, equilibrium behavior, and equal-budget dynamic evolutionary loops, identifying when certified local rank maintenance outperforms global re-evaluation and when it should hand over.

Evaluating new large language models typically requires costly human annotation campaigns at scale. LLM-as-a-judge offers a cheaper alternative, but judge scores carry systematic errors - such as position bias, self-preference, or intransitivity - that can strongly miscalibrate the resulting rankings. We quantify the resulting judge-human disagreement at two complementary levels. At the local level, we estimate per-battle uncertainty from the judge's own score differences by propagating calibrated win probabilities rather than hard labels into the Bradley-Terry procedure. This alone provides a drastic improvement to Elo estimation accuracy, bringing LLM-derived ratings within 17.9 Elo MAE of human-derived ones when averaged over 55 held-out models on LMArena. At the global level, we apply split conformal prediction to the residual gap between LLM-derived and human-derived Elo ratings across held-out models, producing prediction intervals with distribution-free marginal coverage guarantees that account for irreducible LLM-human disagreement. Together, these two layers yield a low-cost evaluation tool that provides developers with calibrated Elo estimates and honest uncertainty bounds, without access to large-scale human annotations. To facilitate reproducibility, we release our code at https://github.com/kargibora/SoftElo .

Multinational companies increasingly require cross-jurisdictional contract review, yet existing legal NLP datasets are largely restricted to a single jurisdiction. We introduce LAUKIN (Legal equivalence dataset of Australia, UK, and INdia), a dataset of clause pairs (AU-UK, UK-IN, IN-AU) labelled for boolean legal equivalence. We develop a novel multi-stage retrieval and reranking pipeline to construct the initial clause pair mapping, with a subset of clause pairs subsequently annotated by legal experts as Equivalent or Not Equivalent. The dataset comprises 14,727 clause pairs from 204 contracts across 8 agreement types, of which 3,000 are manually labelled: 900 train, 600 dev, and 1,500 test. We evaluate 12 models across 4 techniques, achieving a best macro-F1 of 65.11%, establishing LAUKIN as a challenging benchmark. Results reveal that, despite shared legal heritage, drafting conventions diverge significantly across jurisdictions, making cross-jurisdictional equivalence classification non-trivial. LAUKIN also includes 11,727 unlabelled training pairs to support future semi-supervised learning research in legal NLP.

Pairwise comparisons combined with aggregation methods like Elo have become central to evaluating generative models, yet concerns remain that they reward superficial stylistic cues or display judge biases. In a more positive turn, we show that model rankings from pairwise comparisons strongly agree with ground-truth-based accuracy rankings when such ground truth is available for comparison. By converting five well-known benchmarks into free-form generative evaluations, we find that Elo rankings achieve a Spearman correlation above 0.9 with accuracy rankings and substantially outperform direct evaluation when the judge is weak. Furthermore, style and judge bias have only minor effects on model rankings, despite most judgments occurring on pairs where both candidate answers are correct (or incorrect). On such pairs, we find that repetition after the final answer (echo) is a causal driver of judge preference.

We propose Differences in Detection (DnD), an intuitive method to compare two object detection models. Based on the same matching algorithm, it complements the standard metrics of mean Average Precision ($mAP$) and TIDE error analysis with the ability to compare two models directly. More specifically, we calculate the intersection of ground truth labels that are recognized by both models, followed by the corresponding difference sets and the complement set of ground truth labels that are missed by both models. The resulting comparison is more direct and intuitive than a comparison of independent summary statistics. It reveals individual and shared mistakes and becomes particularly interesting when combined with error types. In this case, the differences in detection errors can be analyzed naturally in a standard confusion matrix. While valuable in itself, we believe that one of the best applications of DnD is to guide explainability methods such as ODAM towards metric-relevant examples, grounded in structured subsets. The code for our method is available here: https://github.com/JohannesTheo/differences-in-detection

The ranking of recommendation algorithms is a challenging problem since model performance is sensitive to dataset characteristics such as sparsity, sequential structure, and scale. This drives a demand for a proper methodology for fair comparison between algorithms. Naive aggregation of performance metrics (e.g., averaging NDCG over benchmarks) can yield misleading rankings, undermining practical selection. To address this problem, we introduce a novel, data-driven ranking methodology based on Bradley-Terry (BT) model. We demonstrate that the obtained ranking depends on key dataset statistics. Additionally, we propose a novel metric for evaluating ranking consistency and demonstrate robustness of our ranking to incomplete data. Finally, we introduce a dataset-specific methodology for ranking algorithms on unseen datasets without running the models, relying on extensions of the Bradley-Terry framework, including BT trees and BT models with covariates.

Quantities with measurement units, such as 110 cm and 1.2 m, require language models (LMs) to combine a numeral with a symbolic unit scale. Here, we study how LMs compare such quantities in controlled settings spanning several unit systems. We find that accuracy degrades near the comparison boundary, where small changes in value determine the correct answer. The resulting errors are systematic: linear surrogate models predict LM preferences from numerical-difference and unit-scale-difference cues, and causal interventions on subspaces aligned with these variables shift model's output. The results suggest that LMs compare quantities through a bag of heuristics over numerals and units, rather than first converting both expressions to an exact shared-scale representation.

Many machine learning problems, including similarity learning, ranking, and clustering, rely on empirical pairwise loss functions whose quadratic computational cost quickly becomes prohibitive at scale. We demonstrate how a frugal approach that retains only a fraction of the available information on pairs can achieve estimation or optimization performance comparable to that obtained by using all pairs, by leveraging survey sampling techniques. A central finding, supported by both theory and experiments, is that such sampling plans must target pairs directly rather than individual observations. In particular, for pairwise losses between high-dimensional vectors such as embeddings in vision or graph learning, assigning higher inclusion probabilities to informative pairs using suitable auxiliary information yields performance close to full pairwise evaluation, providing a principled and theoretically grounded trade-off between accuracy and computational cost.

Pairwise preference data is widely used in language-model evaluation and alignment, often for model ranking, reward modeling, or preference optimization. This note formulates a more basic measurement question: given a reference distribution of pairwise preferences, what model-level quantity is estimated when we test whether a model ranks preferred responses above rejected responses? We define pairwise reference alignment as an ordinal observable induced by a model scoring function. Given a reference pair distribution $P_{\mathrm{pair}}$ over triples $(x,y^+,y^-)$, and a scalar model score $S_M(x,y)$, we define the alignment observable as the probability that the model-induced ordering agrees with the reference preference ordering. We further define a centered order-parameter-like statistic and discuss a margin-based extension. The resulting quantities admit simple finite-sample estimators and concentration bounds under independent sampling assumptions. This note does not introduce a new benchmark. It provides a conceptual and statistical formulation for pairwise reference alignment, clarifies the role of the reference pair distribution, and distinguishes the general ordinal observable from scoring choices such as normalized log-probability or energy-based scores. We also provide an initial empirical study on Qwen2.5 models and RewardBench, where the proposed statistics increase with model size and instruction tuning and vary across reference-pair subsets as predicted by the formulation.

Best-of-$N$ sampling is widely used to construct pairwise preference data: $N$ candidates are drawn from a base distribution, and the best is paired with a rejected response. Despite its widespread use, what Bradley--Terry (BT) reward learning extracts from such data, and how to choose $N$ and the base distribution, remain unclear. We specialize a recent analysis of preference data via its induced conditional distribution to Best-of-$N$. For independent-reference variants, we derive closed-form reward targets as explicit functions of $N$ and the base distribution, and show that they preserve the latent reward ranking. For the practical Best-vs-Random and Best-vs-Worst variants, chosen and rejected responses are coupled through the same candidate set, so exact BT representability generally fails; nevertheless, bounded-class minimizers approach the reference targets as $N$ grows. Although margin and connectivity are known to govern sample efficiency in pairwise preference learning, Best-of-$N$ couples them through $N$ in opposing directions: larger $N$ widens pairwise margins but reduces connectivity. This trade-off yields two design principles: use larger $N$ when preference labels are the bottleneck, smaller $N$ when generation is the bottleneck; and shape the base distribution to place mass between the responses whose comparison matters most at test time. Experiments on synthetic and real preference data support the predicted dependence on sample size and base-distribution shape.

In selective classification, a model predicts the labels of data samples where it is confident, and abstains from predicting labels for samples on which it is not confident. The rejected samples are often labeled by an expert, which is expensive. The budget for the expert is best utilized when the model has low error on non-rejected samples. However, the estimate of a model's confidence might be inconsistent with the model's predictions, which can lead to high error on non-rejected points. Such situations can readily occur in in-context binary classification by LLMs. To remedy this, we propose making additional pairwise queries to the same model. These pairwise queries can detect high-error samples and be incorporated into selective classification techniques to reduce the error on non-rejected samples. Theoretically, we establish the conditions under which a simple algorithm using pairwise queries outperforms an inconsistent confidence estimate. We support this insight through extensive experiments for $1$ synthetic and $4$ in-context learning-based real binary classification datasets. In all these cases, we show that our algorithms, using pairwise queries, obtain a better accuracy-cost tradeoff than using only the raw confidence estimates, for instance, the LLM's next-token logits.

Across two public LLM leaderboards, many displayed pairwise rankings do not meet a conventional paired-test resolution target under the actual paired evaluation design: 11 of 40 Open LLM Leaderboard v1 pairwise comparisons and 4 of 9 MMLU-Pro top-10 adjacent-rank pairs are unresolved at (alpha, 1-beta) = (0.05, 0.8). The MMLU-Pro count rises to 6/9 under real subject-level clustering and stays at 5-6 out of 9 in 99.9% of category-bootstrap resamples. We frame paired LLM evaluation as a hypothesis-testing problem, invert level-alpha, power-(1-beta) tests, and report a per-pair resolution ratio q = N/N* as the primary diagnostic. A sharp small-effect expansion with an explicit second-order constant shows that the widely-used unpaired Cohen-h-plus-(1-rho) shortcut deviates from the correct N* by approximately a factor of two in the close-comparison regime, a deficit that three of five off-the-shelf calculators(Cohen 1988, G*Power, R pwr) silently inherit when the user post-multiplies their per-arm output by (1-rho). The unresolved-pair pattern remains under multiplicity correction and anytime-valid sequential testing.

We evaluate whether clinician pairwise preferences provide a reliable signal of clinical safety in large language model (LLM) evaluation using expert feedback from MOOVE (Massive Open Online Validation and Evaluation), a clinician-led platform collecting blinded pairwise preferences alongside multi-criterion rubric ratings. Clinicians assign scores on a discrete $[-2, +2]$ scale, where negative values indicate clinically unsafe or misleading content. Using 26{,}804 pairwise judgments across outputs from 13 LLMs, contributed by more than 736 clinicians across 28+ countries, we find that clinician preference is a poor proxy for safety-critical performance. Models ranking highly under pairwise preference can still exhibit substantial rates of clinically meaningful failures ($\leq -1$) on dimensions such as \emph{Harmlessness} and \emph{Accuracy}. These failures are unevenly distributed across specialties, creating domain-specific ``no-go zones'' not visible in aggregate rankings or single-number leaderboards. We further analyze contributing factors including prompt length, refusal and escalation behavior, and the relative contributions of safety-critical versus surface-level features. A substantial fraction of preference votes carry no positive safety signal, while feature decomposition shows that surface-level characteristics explain slightly more preference variation than safety-critical rubric differences. Finally, we introduce a clinically adjusted preference ranking combining pairwise preference with rubric-derived feedback, producing a more safety-aware ordering than raw Bradley--Terry strength alone. Our findings support evaluation practices that separate preference from safety, report safety-critical failure rates directly, and incorporate clinically grounded adjustments when ranking LLMs for clinical decision making.

Pairwise model comparisons drawn from foundation-model benchmarks ("A is safer than B") are read as quantitative verdicts but hinge on harness choices benchmark papers under-specify. We close one theory-benchmark loop on this primitive: a finite-envelope proposition tying a measurable pairwise-disagreement rate to whether the strict ordering admits a configuration-pair reversal, paired with a commit-stamped evaluation protocol that operationalises it on widely cited alignment benchmarks. On every benchmark we test, configuration choice alone can flip the pairwise verdict; the proposition isolates this strict-reversal failure mode.

Two methodologies dominate current practices of benchmarking: rubric-based scoring evaluates items against predefined criteria, whereas comparative judgment elicits pairwise preferences between outputs. Although both methodologies are widely used, the choice between them is rarely justified. We release JudgmentBench, a benchmark of 30 real-world legal tasks, paired with 1,539 rubric scores and 1,530 pairwise preference judgments collected from practicing attorneys--including at major U.S. law firms--with substantial experience. The annotations constitute the first publicly available dataset in a high-expertise domain in which both supervision signals are elicited from the same experts on the same items. Using LLM-generated outputs at three constructed quality levels, we provide an initial empirical comparison: comparative judgments recover the intended quality ordering substantially better than rubrics under both a per-task rank-correlation metric (mean Spearman's rank correlation of 0.908 vs. 0.150, estimated difference = 0.758 [0.494, 1.021]) and a per-judgment pairwise win-rate metric (0.669 vs. 0.542, estimated difference = 0.127 [0.067, 0.186]), while requiring less than half the annotation time. The patterns hold for human annotators and LLM autograders. Beyond this initial comparison, the paired structure of the dataset supports a broader research agenda on how expert judgment should be elicited, aggregated, and used as supervision in domains without verifiable ground truth.

As interactive LLM-based applications are created and refined, model developers need to evaluate the quality of generated text along many possible axes. For simpler systems, human evaluation may be practical, but in complicated systems like conversational chatbots, the amount of generated text can overwhelm human annotation resources. Model developers have begun to rely heavily on auto-evaluation, where LLMs are also used to judge generation quality. However, existing LLM-as-a-judge benchmarks largely focus on simple Q&A tasks that do not match the complexity of multi-turn conversations. We introduce RankJudge, a benchmark generator for evaluating LLM-as-a-judge on multi-turn conversations grounded in reference documents. RankJudge creates pairs of conversations where one conversation has a single flaw injected into one turn. This construction allows paired conversations to be labeled unambiguously as better or worse, and precisely isolates failure categories to individual turns, enabling a strict joint correctness criterion for judging. We implement RankJudge across the domains of machine learning, biomedicine, and finance, evaluate 21 frontier LLM judges, and rank those judges via the Bradley-Terry model. Our formulation also allows ranking each conversation pair with difficulty ratings, which we use to dynamically curate the evaluation slice to reduce label noise, as confirmed via human annotation. We find that judge rankings are stable under partial observability, coarser correctness criteria, and an alternative random-walk rating algorithm.

Large Multimodal Models (LMMs) have shown promise for video quality assessment, but most methods still predict an absolute score for each video. Such pointwise supervision often mixes perceptual quality with dataset-specific calibration, including annotation protocols, rating habits, and score distributions. As a result, the learned scoring rule may work well within a benchmark but transfer poorly across unseen domains. We argue that relative comparisons alleviate the absolute-scale calibration bias by focusing purely on perceptual differences rather than dataset-specific rating habits. Consequently, we propose \textbf{VersusQ}, a pairwise margin reasoning framework driven entirely by direct comparisons. Specifically, VersusQ performs LMM-based comparison between two videos, reasons about their visual and temporal quality differences, and predicts a signed continuous margin that captures both the preferred choice and the degree of difference. Furthermore, to align interpretable comparison rationales with fine-grained numerical differences, we introduce Margin-Coupled GRPO, which jointly optimizes rollout-based relational reasoning and continuous margin regression. Extensive experiments on multiple public VQA benchmarks demonstrate that VersusQ achieves state-of-the-art performance, strong cross-domain generalization, and reliable fine-grained ranking under heterogeneous evaluation scenarios.

Pairwise preferences and pointwise ratings are the two dominant annotation protocols in image aesthetic assessment (IAA), yet existing benchmarks adopt only one, leaving their complementarity unmeasured under controlled conditions. We introduce PPaint, a matched dual-protocol benchmark in which 15 domain experts, 5 per category, annotate 150 Chinese paintings under both protocols across five aesthetic dimensions, collecting 45,900 pairwise expert judgments through a locally dense preference design alongside the matched ratings. The matched design reveals complementary strengths: preferences yield more consistent ordinal rankings, while ratings anchor the absolute score scale. Fusing both signals via two independent preference-to-score methods yields a fused expert ground truth on which the two constructions converge to nearly identical scores. The same preference-to-score principle extends to label-free VLM training. PSDistill converts VLM pairwise judgments into calibrated pseudo-scores via an Elo reference pool, and trains the same VLM with confidence-weighted ranking optimization to produce a single-pass aesthetic scorer. Trained on a single painting category, the distilled Qwen3-VL-8B improves mean SRCC from 0.504 to 0.709 across all three categories, outperforming all open-source baselines including the dedicated aesthetic model ArtiMuse and matching closed-source Gemini-3.1-Pro within 0.04 SRCC at single-pass inference cost, with cross-domain transfer further validated on APDDv2. We will release the full PPaint dataset and training code.

Pairwise human preference prediction is central to evaluating code-generation systems, where quality often depends on task-specific trade-offs beyond functional correctness. While rubric-based LLM judges improve interpretability by decomposing evaluation into explicit criteria, most existing pipelines remain pointwise: they score each response independently and derive preferences by comparing aggregated scores. We show that this design is poorly matched to pairwise code preference prediction and can underperform a strong monolithic judge. We propose CriterAlign, a criterion-centric framework that adapts rubric-based judging to pairwise preference evaluation through direct criterion-level pairwise judgments, tie-driven criterion refinement, swap-consistency filtering, and final pairwise synthesis. We further introduce Human-Preference-Aligned Guidance (HPAG), synthesized offline from training examples by extracting recurring rationale gaps between human preferences and monolithic judge predictions, and injected into the criterion generator, criterion judge, and final judge. On BigCodeReward, CriterAlign improves a Qwen2.5-VL-32B monolithic judge from 60.4% to 66.3% accuracy, with ablations confirming the contributions of pairwise criterion design and HPAG.

Pairwise image quality assessment (IQA) in professional photography requires a model not only to identify the preferred image between two candidates, but also to provide convincing and image-grounded reasoning. In the NTIRE 2026 RAIM challenge, this requirement is further emphasized by jointly evaluating preference prediction and rationale generation. To address this task, we propose iDiff, an Interpretable Difference-aware framework for pairwise image quality assessment. Our method adopts a dual-branch design consisting of an Answer Model and a Thinking Model. The Answer Model performs robust preference prediction by explicitly decomposing each sample into left/right global and local views, followed by content-aware specialization for person and scene images and ensemble-based aggregation across backbones. The Thinking Model focuses on rationale generation and is progressively enhanced with expert-style templates, multi-source quality features, and answer-aware supervision conditioned on the Answer Model prediction. In this way, iDiff jointly models discriminative decision making and structured explanation, improving both robustness and interpretability. Extensive experiments demonstrate the effectiveness of the proposed framework on both accuracy and reasoning-quality metrics. Our method achieved first place in the NTIRE 2026 RAIM challenge, showing the effectiveness of integrating explicit difference modeling with structured multimodal reasoning for pairwise IQA.

Parallel reasoning, where a generator samples many candidate solutions and an aggregator selects the best, is one of the most effective forms of test-time scaling in large language models, and pairwise self-verification has become its strongest aggregation primitive. Yet pairwise verification carries a heavy cost: each judgment reads two complete solutions in full, and existing methods perform tens of such judgments per problem regardless of whether the comparison is informative. We introduce CAPS (Cascaded Adaptive Pairwise Selection), an inference-only framework that allocates verifier compute non-uniformly along two orthogonal axes: an evidence axis that adapts how much of each candidate the judge sees, and a distribution axis that adapts how comparisons are spread across the pool. CAPS instantiates these into a four-stage cascade with an optional rescue subroutine, and admits a closed-form verifier-token cost in which the per-candidate marginal cost is roughly halved relative to uniform full-evidence schedules. On four self-verifying models (Qwen3-14B, GPT-OSS-20B, Qwen3-4B-Instruct/Thinking) and five reasoning benchmarks spanning code (LiveCodeBench-v5/v6, CodeContests) and math (AIME 2025, HMMT 2025), CAPS outperforms the leading pairwise verifier on 14 of 20 suites while using 25.4% of its verifier-token budget on code, and outperforms pointwise self-verification on all 20. The trade-off suites admit an interpretable diagnostic in terms of the verifier's accuracy at partial versus full evidence, providing a concrete pre-deployment check for cascade suitability.

Test-time compute scaling is a primary axis for improving LLM reasoning. Existing methods primarily scale depth by extending a single reasoning trace. Scaling breadth by sampling multiple candidates in parallel is straightforward, but introduces a selection bottleneck: choosing the best candidate without a ground-truth verifier, since pointwise LLM judging is noisy and biased. To address this, we introduce OpenDeepThink, a population-based test-time compute framework that selects via pairwise Bradley-Terry comparison. Each generation, the LLM judges random pairs of candidates and aggregates votes via Bradley-Terry into a global ranking; top-ranked candidates are preserved and the top three quarters are mutated using the natural-language critiques produced during comparison; the bottom quarter is discarded. OpenDeepThink raises Gemini 3.1 Pro's effective Codeforces Elo by +405 points in eight sequential LLM-call rounds (~27 minutes wall-clock). The pipeline transfers across weaker and stronger models without retuning, and on the multi-domain HLE benchmark, gains appear concentrated in objectively verifiable domains and reverse in subjective ones. We release CF-73, a curated set of 73 expert-rated Codeforces problems with International Grandmaster annotation and 99% local-evaluation agreement against the official verdict.

Shapley value and its priority-aware extensions are widely used for valuation in machine learning, but existing methods require pairwise priority to be binary and acyclic, a restriction spectacularly violated in real-data examples such as aggregated human preferences and multi-criterion comparisons. We introduce the generalized priority-aware Shapley value (GPASV), a random order value defined on arbitrary directed weighted priority graphs, in which pairwise edges penalize rather than forbid order violations. GPASV covers a range of classical models as boundary cases. We establish GPASV through an axiomatic characterization, develop the associated computational methods, and introduce a priority sweeping diagnostic extending PASV's. We apply GPASV to LLM ensemble valuation on the cyclic Chatbot Arena preference graph, illustrating that priority-aware valuation is not a one-button operation: different balances of pairwise graph priority versus individual soft priority produce substantively different valuations of the same data.

Pairwise Ranking Prompting (PRP) elicits pairwise preference judgments from an LLM, which are then aggregated into a ranking, usually via classical sorting algorithms. However, judgments are noisy, order-sensitive, and sometimes intransitive, so sorting assumptions do not match the setting. Because sorting aims to recover a full permutation, truncating it to meet a call budget does not produce a dependable top-K. We thus reframe PRP reranking as active learning from noisy pairwise comparisons and show that active rankers are drop-in replacements that improve NDCG@10 per call in the call-constrained regime. Our noise-robust framework also introduces a randomized-direction oracle that uses a single LLM call per pair. This approach converts systematic position bias into zero-mean noise, enabling unbiased aggregate ranking without the cost of bidirectional calls.

LLM-as-a-judge is now the default measurement instrument for open-ended generation, but on the public JudgeBench benchmark even strong instruction-tuned judges barely scrape past random on objective-correctness pairwise items. We introduce RTLC, a three-stage prompting recipe -- Research, Teach-to-Learn, Critique -- that promotes a single black-box LLM into an ensemble-of-thought judge with no fine-tuning, retrieval, or external tools. Stage 1 wraps the input in a fixed pedagogical scaffold porting the Feynman Learning Technique (study $\to$ teach $\to$ find gaps $\to$ simplify) into LLM prompting. Stage 2 draws N=10 independent candidate verdicts at temperature 0.4. Stage 3 acts as its own critic, cross-comparing the candidate set against the original question to emit one critiqued verdict at temperature 0. On JudgeBench-GPT (350 hard pairwise items), Claude 3.7 Sonnet's pairwise accuracy climbs from 64.6% (single-shot vanilla prompt) to 78.6% (RTLC critique-of-10) -- an absolute 14.0-percentage-point gain. RTLC also beats N=10 self-consistency majority voting (77.7%) and a zero-shot first candidate (74.0%). A clean three-step ablation attributes +9.4 pp to the Teach-to-Learn scaffold, +3.7 pp to N=10 marginalisation, and +0.9 pp to explicit critique. We discuss the cost-accuracy frontier (RTLC sits above self-consistency at every working point), the error-budget breakdown across the four JudgeBench categories (knowledge, reasoning, math, coding), and how RTLC composes orthogonally with post-hoc judge-score calibration, with the two interventions compounding multiplicatively in practice.

Organizations increasingly deploy multiple AI systems across task domains, but selecting a small, high-performing ensemble can require costly model calls, benchmark runs, and human evaluation. We study this selection problem as a distributional variant of multiwinner voting: tasks are drawn from an unknown domain distribution, each task induces feedback over candidate experts, and a committee's value on a task is determined by its best-performing member. We analyze both binary feedback, for tasks with correct/incorrect outcomes, and pairwise feedback, for tasks where candidate outputs are compared by preference. In the binary setting, the induced objective is coverage. We give exhaustive-elicitation baselines and matching worst-case query lower bounds, and we design a failure-conditioned greedy algorithm that preserves the standard $(1-1/e)$ guarantee while obtaining instance-dependent query savings. In the pairwise setting, we study $θ$-winning committees. We show that full-information optimization admits a PTAS but no EPTAS under Gap-ETH, and that the objective is monotone but not submodular. This motivates a weighted ordinal coverage relaxation, which is submodular and supports a failure-conditioned greedy oracle under pairwise feedback. We then convert this oracle back into $θ$-type guarantees through finite-family auditing or a minimax wrapper. We also provide small-scale LLM experiments illustrating the predicted query savings and the role of complementarity in committee selection.

Raw cosine in the 768-dimensional output space of the Contrastive Style Descriptor (CSD) is now widely read as an absolute, calibrated style-fidelity score for text-to-image and style-imitation evaluation. We introduce the discrimination gap, a corpus-internal, prototype-free and threshold-free diagnostic that tests whether contrastive style cosines admit an absolute same-versus-different interpretation on a candidate artist corpus. On a 1799-artwork, 91-artist public-domain corpus, raw CSD cosine yields negative point-estimate gaps for $23/91$ artists at the pairwise level ($2/91$ robust under bootstrap) and for $15/91$ in the aggregated-pool scoring regime style-fidelity evaluations typically use. CSLS readout on the frozen backbone reduces the aggregated negative-gap count to $4/91$; combined with positional-embedding interpolation to $336$ pixels it raises unsupervised pair-verification AUC from $0.883$ to $0.905$ across $25$ artist-disjoint splits. We refer to this diagnostic-driven readout protocol on the frozen backbone (CSLS as default, pos-interp $336$ as the stronger optional setting) as CSD+, not a new encoder.A cross-backbone check on CLIP-ViT-L/14, SigLIP-large and DINOv2-Large reproduces the same shared-tradition failure pattern, providing evidence that the residual reflects a shared limitation of the four backbones we tested rather than a CSD-specific artefact. Practical implication: before reporting CSD cosine as an absolute style-fidelity score, run the diagnostic on the candidate corpus; CSLS is the minimal correction when it fails.

A series of papers has introduced the Heuristic Rating Estimation method, which evaluates a set of alternatives based on pairwise comparisons and the weights of reference alternatives. We formulate the conditions under which the HRE method can be applied correctly. The research considers both arithmetic and geometric algorithms for complete and incomplete pairwise comparison methods. The illustrative examples show that the estimations of inconsistency in the arithmetic variant are optimal.

Measuring the breadth of a word's meaning, or its spread across contexts, has become feasible with contextualized token embeddings. A word type can be represented as a cloud of token vectors, with dispersion-based statistics serving as proxies for contextual diversity (Nagata and Tanaka-Ishii, ACL2025). These measurements are useful for deciding appropriate sense distinctions when constructing thesauri and domain-specific dictionaries. However, when comparing the breadth of two word types, naive hypothesis testing on dispersion can be misleading: differences in semantic direction can masquerade as dispersion differences, inflating Type-I error and yielding "statistically significant" outcomes even when there is no true breadth difference. This is problematic because significance testing should distinguish genuine effects from incidental fluctuations in small-difference regimes. We propose a Householder-aligned permutation test to isolate dispersion differences from directional differences. Our method applies a single Householder reflection to align the mean directions of the two word types and then performs a permutation test on the aligned token clouds, yielding calibrated, non-parametric p-values. For practicality, we introduce a GPU-oriented implementation that batches permutations and linear algebra operations. Empirically, our alignment reduced Type-I error by 32.5% while preserving sensitivity to genuine breadth differences, and achieved a 23x speedup over the CPU baseline.

Ranking LLMs via pairwise human feedback underpins current leaderboards for open-ended tasks, such as creative writing and problem-solving. We analyze ~89K comparisons in 116 languages from 52 LLMs from Arena, and show that the best-fit global Bradley-Terry (BT) ranking is misleading. Nearly 2/3 of the decisive votes cancel out, and even the top 50 models according to the global BT ranking are statistically indistinguishable (pairwise win probabilities are at most 0.53 within the top 50 models). We trace this failure to strong, structured heterogeneity of opinions across language, task, and time. Moreover, we find an important characteristic - language plays a key role. Grouping by language (and families) increases the agreement of votes massively, resulting in two orders of magnitude higher spread in the ELO scores (i.e., very consistent rankings). What appears as global noise is in fact a mixture of coherent but conflicting subpopulations. To address such heterogeneity in supervised machine learning, we introduce the framework of $(λ, ν)$-portfolios, which are small sets of models that achieve a prediction error at most $λ$, "covering" at least a $ν$ fraction of users. We formulate this as a variant of the set cover problem and provide guarantees using the VC dimension of the underlying set system. On the Arena data, our algorithms recover just 5 distinct BT rankings that cover over 96% of votes at a modest $λ$, compared to the 21% coverage by the global ranking. We also provide a portfolio of 6 LLMs that cover twice as many votes as the top-6 LLMs from a global ranking. We further construct portfolios for a classification problem on the COMPAS dataset using an ensemble of fairness-regularized classification models and show that these portfolios can be used to detect blind spots in the data, which might be of independent interest to policymakers.