Consistencies in Social Ranking

2026-03-18

AI Summary

This study addresses the core challenge in social ranking—how to fairly order individuals’ performances across coalitions when only partial comparability among coalitions is available. By adopting an axiomatic approach, the paper introduces a novel consistency concept tailored to variable coalition domains and demonstrates its pivotal role in distinguishing prominent ranking solutions. The authors develop a classification framework grounded in key axioms, including consistency and invariance, and rigorously establish their logical independence. Through a systematic evaluation of existing ranking methods, the work elucidates how these axioms fundamentally shape the characterization of ranking rules, thereby providing a unified theoretical foundation and analytical framework for social ranking problems.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Game Theory and Economic Paradigms: Social Choice / Voting
• Knowledge Representation and Reasoning: Preferences

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Ranking individuals based on their performance in different coalitions is a problem emerging in various domains (teams sports, scientific evaluation, argumentation, etc.). Often, for practical reasons, the number of comparable coalitions is limited. Therefore, the foundational principles of ranking solutions must support realistic interpretations in contexts where only certain coalitions can be compared. To address this issue, in this paper we present an axiomatic analysis of solutions for the social ranking problem centered on the notion of consistency. More precisely, we show that an appropriate notion of consistency, which specifies how to combine rankings on individuals across different rankings on coalitions, plays a key role in any axiomatic characterization, representing the true distinguishing feature of each solution. This role is further highlighted by the taxonomy of the complementary axioms used in our characterizations, which boil down to well-studied properties of invariance with respect to the label of players or coalitions, and also with respect to minor changes in a coalitional ranking. By showing the logical independence of the axioms used in each characterization, as well as a rigorous analysis of alternative notions of consistency with respect to the majority of solutions from the literature, this work attempts to provide a first systematic study of the social ranking problem over a variable domain of coalitions.

Problem

• social ranking
• coalitional ranking
• consistency
• axiomatic analysis
• performance evaluation

Innovation

• consistency
• axiomatic characterization
• social ranking
• coalitional ranking
• invariance