Abstract
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 Ppair over triples (x,y+,y−), and a scalar model score SM(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.
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Language model benchmarks are pervasive and computationally-efficient proxies for real-world performance. However, many recent works find that benchmarks often fail to predict real utility. Towards bridging this gap, we introduce benchmark alignment, where we use limited amounts of information about model performance to automatically update offline benchmarks, aiming to produce new static benchmarks that predict model pairwise preferences in given test settings. We then propose BenchAlign, the first solution to this problem, which learns preference-aligned weightings for benchmark questions using the question-level performance of language models alongside ranked pairs of models that could be collected during deployment, producing new benchmarks that rank previously unseen models according to these preferences. Our experiments show that our aligned benchmarks can accurately rank unseen models according to models of human preferences, even across different sizes, while remaining interpretable. Overall, our work provides insights into the limits of aligning benchmarks with practical human preferences, which stands to accelerate model development towards real utility.
Marco Gutierrez, Xinyi Leng, Hannah Cyberey +3
May 25, 2026cs.LG
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.
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We study learning a mixture of
k Plackett-Luce models from multi-way ranking responses from annotators that may represent heterogeneous underlying preferences. This problem has many applications in AI alignment and preference optimization. Prior work has studied mixtures of Bradley-Terry models from pairwise comparisons. However, estimating a mixture of multi-way ranking models can become theoretically unidentifiable when
k exceeds
m/2, where
m is the ranking length. We design an efficient algorithm to address this issue by first augmenting the rankings to a larger size (e.g., generating comparisons from a base model), followed by a gradient-based estimation to reduce inference cost (in the input embedding space). With this procedure in mind, we then fit a mixture of Plackett-Luce (PL) models via an expectation-maximization-style iteration, or MoPLEx in short. We conduct extensive experiments to verify this algorithm. First, we find that the gradient-based approximation estimates true probabilities with less than 5% error on models with up to 34 billion parameters. Second, MoPLEx improves clustering and ranking accuracy by an average of 43.7% and 15.2% over baselines using a single PL model or a mixture of Bradley-Terry models, on UltraFeedback and PERSONA datasets. These results demonstrate the effectiveness of MoPLEx for tackling multi-way rankings following heterogeneous preferences through measuring alignment via gradients.
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