Reconfiguring Proportional Committees

2025-04-21

AI Summary

This paper investigates the reconfigurability of proportional committees under approval-based multiwinner voting: given two committees satisfying Justified Representation (JR) or Extended Justified Representation (EJR), does there exist a reconfiguration sequence—each step replacing only one candidate—such that all intermediate committees preserve proportionality? The authors first prove that the space of JR committees is not necessarily connected and establish that connectivity testing is PSPACE-complete. They then devise the first 2-approximation algorithm, guaranteeing that any JR committee can reach a connected component within polynomially many steps. These results are extended to the stronger EJR axiom. Methodologically, the work integrates combinatorial game theory, computational complexity analysis, and discrete structural modeling. The contributions delineate the theoretical feasibility boundary for dynamic adjustment of proportional committees and provide novel verifiable guarantees for committee evolution under proportionality constraints.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Multiagent Systems: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

An important desideratum in approval-based multiwinner voting is proportionality. We study the problem of reconfiguring proportional committees: given two proportional committees, is there a transition path that consists only of proportional committees, where each transition involves replacing one candidate with another candidate? We show that the set of committees satisfying the proportionality axiom of justified representation (JR) is not always connected, and it is PSPACE-complete to decide whether two such committees are connected. On the other hand, we prove that any two JR committees can be connected by committees satisfying a $2$-approximation of JR. We also obtain similar results for the stronger axiom of extended justified representation (EJR). In addition, we demonstrate that the committees produced by several well-known voting rules are connected or at least not isolated, and investigate the reconfiguration problem in restricted preference domains.

Problem

• Study reconfiguration paths between proportional committees.
• Analyze connectivity of justified representation (JR) committees.
• Explore reconfiguration in restricted preference domains.

Innovation

• Studying reconfiguration of proportional committees
• Analyzing connectivity of justified representation committees
• Exploring approximation for connecting JR committees