We present an axiomatic study of various solutions to the social ranking problem, where a solution links any ranking of coalitions of players to a binary relation between individual players. We focus on solutions that align with the desirability relation, asserting that player i is more desirable than player j if any coalition including i but not j ranks higher than the corresponding coalition formed by replacing i with j. Unlike previous characterizations, our study highlights the central role of the desirability property as a foundational axiom in the characterization of five solutions from the related literature: Ceteris Paribus majority, lexicographic excellence and its dual, $$L^{(1)}$$ L ( 1 ) solution and its dual. Our main results reveal additional similarities among these five solutions and emphasize the essential features that should be considered when selecting the most appropriate solution for a given scenario. A practical application involving a bicameral legislature is also presented.

We consider a learning augmented framework for NP-hard permutation problems. The algorithm has access to predictions telling, given a pair $u,v$ of elements, whether $u$ is before $v$ or not in an...

In this work, we investigate the merits of explicitly optimizing for inference time algorithmic performance during model training. We show how optimizing for inference time performance can improve...

Large language models (LLMs) deployed as agents solve user-specified tasks over multiple steps while keeping the required manual engagement to a minimum. Crucially, such LLMs need to ground their...

As large language models increasingly drive real-world applications, aligning them with human values becomes paramount. Reinforcement Learning from Human Feedback (RLHF) has emerged as a key...

Circular and non-flat data distribution are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A...

This paper introduces von Mises-Fisher exploration (vMF-exp), a scalable method for exploring large action sets in reinforcement learning problems where hyperspherical embedding vectors represent...

Increasing diversity in language models is a challenging yet essential objective. A common approach is to raise the decoding temperature. In this work, we investigate this approach through a...

Traditional online file management systems, such as Google Drive and OneDrive, provide convenient platforms for collaborative editing and sharing, but they come with inherent limitations. These systems often offer limited storage space and operate on centralized...

Riemannian methods have established themselves as state-of-the-art approaches in Brain-Computer Interfaces (BCI) in terms of performance. However, their adoption by experimenters is often hindered by a lack of interpretability. In this work, we propose a set of tools designed to enhance practitioners' understanding of the decisions made by Riemannian methods. Specifically, we develop techniques to quantify and visualize the influence of the different sensors on classification outcomes. Our approach includes a visualization tool for high-dimensional covariance matrices, a classifieragnostic tool that focuses on the classification process, as well as methods that leverage the data's topology to better characterize the role of each sensor. We demonstrate these tools on a specific dataset and provide Python code to facilitate their use by practitioners, thereby promoting the adoption of Riemannian methods in BCI.