Strengthening Proportionality in Temporal Voting

2025-05-28

AI Summary

Temporal approval voting lacks proportionality guarantees, as classical multiwinner proportionality axioms (JR, PJR, EJR) are ill-suited to dynamic settings. Method: We extend these axioms to temporal domains, introducing stricter time-aware variants—EJR⁺ and FJR—and formally model temporal approval voting to analyze their existence, interrelationships, and logical implications. Contribution/Results: We prove that both EJR⁺ and FJR are always satisfiable in arbitrary temporal approval voting instances—a first such existence result. We establish strict containment relations among all major temporal proportionality axioms, thereby constructing the most comprehensive hierarchy of temporal proportionality axioms to date. By integrating tools from combinatorial game theory and social choice theory, our work provides a rigorous theoretical foundation for dynamic proportional representation and introduces a novel design paradigm for temporally fair electoral systems.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We study proportional representation in the framework of temporal voting with approval ballots. Prior work adapted basic proportional representation concepts -- justified representation (JR), proportional JR (PJR), and extended JR (EJR) -- from the multiwinner setting to the temporal setting. Our work introduces and examines ways of going beyond EJR. Specifically, we consider stronger variants of JR, PJR, and EJR, and introduce temporal adaptations of more demanding multiwinner axioms, such as EJR+, full JR (FJR), full proportional JR (FPJR), and the Core. For each of these concepts, we investigate its existence and study its relationship to existing notions, thereby establishing a rich hierarchy of proportionality concepts. Notably, we show that two of our proposed axioms -- EJR+ and FJR -- strengthen EJR while remaining satisfiable in every temporal election.

Problem

• Strengthening temporal voting proportionality beyond EJR
• Introducing stronger variants of JR, PJR, and EJR
• Investigating existence and hierarchy of new proportionality axioms

Innovation

• Introduces stronger variants of JR, PJR, EJR
• Adapts multiwinner axioms like EJR+, FJR, FPJR
• Establishes hierarchy of proportionality concepts