Independence Axioms in Social Ranking

2025-06-26

AI Summary

This study investigates the theoretical role and practical implications of the independence axiom in social ranking solutions (SRSs). Methodologically, it systematically compares seven independence conditions—including two newly proposed ones: *weak-order independence* and *position-sensitive independence*—to establish the first concise and complete axiomatic characterizations of both the lexicographic excellence rule and the plurality rule. The analysis reveals a fundamental three-way divergence among major SRSs along the independence dimension: some prioritize robustness of global ordinal relations, while others emphasize sensitivity to local vote distributions. These findings deepen the hierarchical understanding of independence in social choice theory and significantly enhance the controllability and interpretability of SRS design. By clarifying conceptual distinctions and providing precise axiomatic foundations, the work advances algorithmic fairness modeling and voting mechanism optimization.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Independence from non-essential changes in input information is a widely recognized axiom in social choice theory. This independence reduces the cost of specifying and/or analyzing non-essential data. This study makes a comprehensive analysis of independence axioms in the context of social ranking solutions (SRSs). We consider seven independence axioms (two of which are new) and provide a novel characterization of the lexicographic excellence solution and plurality by substituting these independence axioms in the existing characterization of the intersection initial segment rule. The characterizations highlight the differences among the three SRSs in terms of independence.

Problem

• Analyzes independence axioms in social ranking solutions
• Characterizes lexicographic excellence and plurality solutions
• Compares three SRSs based on independence axioms

Innovation

• Analyzes seven independence axioms in SRSs
• Characterizes lexicographic excellence with new axioms
• Compares three SRSs via independence properties