Evaluating large language models (LLMs) on open-ended tasks without ground-truth labels is increasingly done via the LLM-as-a-judge paradigm. A critical but under-modeled issue is that judge LLMs differ substantially in reliability; treating all judges equally can yield biased leaderboards and misleading uncertainty estimates. More data can make evaluation more confidently wrong under misspecified aggregation. We propose a judge-aware ranking framework that extends the Bradley-Terry-Luce model by introducing judge-specific discrimination parameters, jointly estimating latent model quality and judge reliability from pairwise comparisons without reference labels. We establish identifiability up to natural normalizations and prove consistency and asymptotic normality of the maximum likelihood estimator, enabling confidence intervals for score differences and rank comparisons. Across multiple public benchmarks and a newly collected dataset, our method improves agreement with human preferences, achieves higher data efficiency than unweighted baselines, and produces calibrated uncertainty quantification for LLM rankings.

Large language models are often ranked according to their level of alignment with human preferences---a model is better than other models if its outputs are more frequently preferred by humans. One of the popular ways to elicit human preferences utilizes pairwise comparisons between the outputs provided by different models to the same inputs. However, since gathering pairwise comparisons by humans is costly and time-consuming, it has become a common practice to gather pairwise comparisons by a strong large language model---a model strongly aligned with human preferences. Surprisingly, practitioners cannot currently measure the uncertainty that any mismatch between human and model preferences may introduce in the constructed rankings. In this work, we develop a statistical framework to bridge this gap. Given a (small) set of pairwise comparisons by humans and a large set of pairwise comparisons by a model, our framework provides a rank-set---a set of possible ranking positions---for each of the models under comparison. Moreover, it guarantees that, with a probability greater than or equal to a user-specified value, the rank-sets cover the true ranking consistent with the distribution of human pairwise preferences asymptotically. Using pairwise comparisons made by humans in the LMSYS Chatbot Arena platform and pairwise comparisons made by three strong large language models, we empirically demonstrate the effectivity of our framework and show that the rank-sets constructed using only pairwise comparisons by the strong large language models are often inconsistent with (the distribution of) human pairwise preferences.

However, existing RLHF models are considered inefficient as they produce only a single preference data from each human feedback. To tackle this problem, we propose a novel RLHF framework called SeqRank, that uses sequential preference ranking to enhance the feedback efficiency. Our method samples trajectories in a sequential manner by iteratively selecting a defender from the set of previously chosen trajectories $\mathcal{K}$ and a challenger from the set of unchosen trajectories $\mathcal{U}\setminus\mathcal{K}$, where $\mathcal{U}$ is the replay buffer. We propose two trajectory comparison methods with different defender sampling strategies: (1) sequential pairwise comparison that selects the most recent trajectory and (2) root pairwise comparison that selects the most preferred trajectory from $\mathcal{K}$. We construct a data structure and rank trajectories by preference to augment additional queries. The proposed method results in at least 39.2% higher average feedback efficiency than the baseline and also achieves a balance between feedback efficiency and data dependency. We examine the convergence of the empirical risk and the generalization bound of the reward model with Rademacher complexity. While both trajectory comparison methods outperform conventional pairwise comparison, root pairwise comparison improves the average reward in locomotion tasks and the average success rate in manipulation tasks by 29.0% and 25.0%, respectively. The source code and the videos are provided in the supplementary material.

In this work, we study how to efficiently obtain perfect samples from a discrete distribution $\mathcal{D}$ given access only to pairwise comparisons of elements of its support. Specifically, we assume access to samples $(x, S)$, where $S$ is drawn from a distribution over sets $\mathcal{Q}$ (indicating the elements being compared), and $x$ is drawn from the conditional distribution $\mathcal{D}_S$ (indicating the winner of the comparison) and aim to output a clean sample $y$ distributed according to $\mathcal{D}$. We mainly focus on the case of pairwise comparisons where all sets $S$ have size 2. We design a Markov chain whose stationary distribution coincides with $\mathcal{D}$ and give an algorithm to obtain exact samples using the technique of Coupling from the Past. However, the sample complexity of this algorithm depends on the structure of the distribution $\mathcal{D}$ and can be even exponential in the support of $\mathcal{D}$ in many natural scenarios. Our main contribution is to provide an efficient exact sampling algorithm whose complexity does not depend on the structure of $\mathcal{D}$. To this end, we give a parametric Markov chain that mixes significantly faster given a good approximation to the stationary distribution. We can obtain such an approximation using an efficient learning from pairwise comparisons algorithm (Shah et al., JMLR 17, 2016). Our technique for speeding up sampling from a Markov chain whose stationary distribution is approximately known is simple, general and possibly of independent interest.

We consider the classical problem of finding the minimum feedback arc set on tournaments (MFAST). The problem is NP-hard in general and we study it for important classes of tournaments that arise naturally in the problem of learning to rank from pairwise comparisons. Specifically, we consider tournaments classes that arise out of parametric preference matrices that can lead to cyclic preference relations. We investigate their structural properties via forbidden sub tournament configurations. Towards this, we introduce \emph{Tournament Dimension} - a combinatorial parameter that characterizes the size of a forbidden configuration for rank $r$ tournament classes i.e., classes that arise out pairwise preference matrices which lead to rank $r$ skew-symmetric matrices under a suitable link function.

The literature on ranking from ordinal data is vast, and there are several ways to aggregate overall preferences from pairwise comparisons between objects. In particular, it is well-known that any Nash equilibrium of the zero-sum game induced by the preference matrix defines a natural solution concept (winning distribution over objects) known as a von Neumann winner. Many real-world problems, however, are inevitably multi-criteria, with different pairwise preferences governing the different criteria. In this work, we generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability. Our framework allows for non-linear aggregation of preferences across criteria, and generalizes the linearization-based approach from multi-objective optimization. From a theoretical standpoint, we show that the Blackwell winner of a multi-criteria problem instance can be computed as the solution to a convex optimization problem. Furthermore, given random samples of pairwise comparisons, we show that a simple, plug-in estimator achieves (near-)optimal minimax sample complexity. Finally, we showcase the practical utility of our framework in a user study on autonomous driving, where we find that the Blackwell winner outperforms the von Neumann winner for the overall preferences.

Pairwise evaluation of large language models (LLMs) has become the dominant paradigm for benchmarking open-ended tasks, yet non-transitive preferences, where evaluators prefer A over B, B over C, but C over A, fundamentally undermine ranking reliability. We show that this critical issue stems largely from low-quality data that contains inherently ambiguous preference pairs. To address this challenge, we propose ELSPR, a principled graph-theoretic framework that models pairwise preferences as tournament graphs and systematically identifies problematic training data. ELSPR quantifies non-transitivity through strongly connected components (SCCs) analysis and measures overall preference clarity using a novel normalized directed graph structural entropy metric. Our filtering methodology selectively removes preference data that induce non-transitivity while preserving transitive preferences. Extensive experiments on the AlpacaEval benchmark demonstrate that models fine-tuned on ELSPR-filtered data achieve substantial improvements: a 13.8% reduction in non-transitivity, a 0.088 decrease in structural entropy, and significantly enhanced discriminative power in real-world evaluation systems. Human validation confirms that discarded data exhibit dramatically lower inter-annotator agreement (34.4% vs. 52.6%) and model-human consistency (51.2% vs. 80.6%) compared to cleaned data. These findings establish ELSPR as an effective data self-purification approach for developing more robust, consistent, and human-aligned LLM evaluation systems.

Comprehensive, unbiased, and comparable evaluation of modern generalist policies is uniquely challenging: existing approaches for robot benchmarking typically rely on heavy standardization, either by specifying fixed evaluation tasks and environments, or by hosting centralized ''robot challenges'', and do not readily scale to evaluating generalist policies across a broad range of tasks and environments. In this work, we propose RoboArena, a new approach for scalable evaluation of generalist robot policies in the real world. Instead of standardizing evaluations around fixed tasks, environments, or locations, we propose to crowd-source evaluations across a distributed network of evaluators. Importantly, evaluators can freely choose the tasks and environments they evaluate on, enabling easy scaling of diversity, but they are required to perform double-blind evaluations over pairs of policies. Then, by aggregating preference feedback from pairwise comparisons across diverse tasks and environments, we can derive a ranking of policies. We instantiate our approach across a network of evaluators at seven academic institutions using the DROID robot platform. Through more than 600 pairwise real-robot evaluation episodes across seven generalist policies, we demonstrate that our crowd-sourced approach can more accurately rank the performance of existing generalist policies than conventional, centralized evaluation approaches, while being more scalable, resilient, and trustworthy. We open our evaluation network to the community and hope that it can enable more accessible comparisons of generalist robot policies.