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.

In this work, we generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability.

In this work, we generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability.

Additional Feedback: Some of the major/minor concerns in chronological order are as follows: 1. Please mention the citation for Condorset winner and Borda winner when you first mention them in the introduction. The authors acknowledge this aspect, anyway in the paper. In my opinion, this makes the results fairly restrictive. After the authors propose Blackwell winner, the paper's novelty seem to be fairly limited. The analysis job is well-done.

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.

We introduce a multiple criteria Bayesian preference learning framework incorporating behavioral cues for decision aiding. The framework integrates pairwise comparisons, response time, and attention duration to deepen insights into decision-making processes. The approach employs an additive value function model and utilizes a Bayesian framework to derive the posterior distribution of potential ranking models by defining the likelihood of observed preference data and specifying a prior on the preference structure. This distribution highlights each model's ability to reconstruct Decision-Makers' holistic pairwise comparisons. By leveraging both response time as a proxy for cognitive effort and alternative discriminability as well as attention duration as an indicator of criterion importance, the proposed model surpasses traditional methods by uncovering richer behavioral patterns. We report the results of a laboratory experiment on mobile phone contract selection involving 30 real subjects using a dedicated application with time-, eye-, and mouse-tracking components. We validate the novel method's ability to reconstruct complete preferences. The detailed ablation studies reveal time- and attention-related behavioral patterns, confirming that integrating comprehensive data leads to developing models that better align with the DM's actual preferences.

Group decision-making is becoming increasingly common in areas such as education, dining, travel, and finance, where collaborative choices must balance diverse individual preferences. While conventional recommender systems are effective in personalization, they fall short in group settings due to their inability to manage conflicting preferences, contextual factors, and multiple evaluation criteria. This study presents the development of a Context-Aware Multi-Criteria Group Recommender System (CA-MCGRS) designed to address these challenges by integrating contextual factors and multiple criteria to enhance recommendation accuracy. By leveraging a Multi-Head Attention mechanism, our model dynamically weighs the importance of different features. Experiments conducted on an educational dataset with varied ratings and contextual variables demonstrate that CA-MCGRS consistently outperforms other approaches across four scenarios. Our findings underscore the importance of incorporating context and multi-criteria evaluations to improve group recommendations, offering valuable insights for developing more effective group recommender systems.

The paper studied preference aggregation via pairwise comparisons along multiple criteria. All reviewers find the problem setup interesting and appreciate the theoretical contribution novelty. I also share this sentiment, and find the paper a pleasure to read. The authors are strongly encouraged to take into account the reviews, in particular, to further strengthen the empirical analysis and discussions if possible, when preparing a revision.

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.