Committee Monotonicity and Proportional Representation for Ranked Preferences

2024-06-28

AI Summary

This paper addresses the long-standing open problem of reconciling fairness and monotonicity in committee elections under ordinal preferences—specifically, how to simultaneously satisfy proportional justified representation (PSC), committee monotonicity, and independence of losing voter groups under partial (truncated) preference information. We propose Solid Coalition Refinement (SCR), the first voting rule satisfying Dummett’s PSC, inclusion-based PSC, and committee monotonicity, achieved via ordinal modeling and refinement over solid coalitions. We refute Graham-Squire et al.’s conjecture that PSC is unattainable under truncation, proving instead that SCR satisfies both PSC and independence of losing groups even with truncated preferences. Furthermore, we systematically establish fundamental incompatibilities between several prominent fairness axioms—including various forms of proportional representation—and committee monotonicity, thereby delineating sharp boundaries for feasible axiomatizations in truncated-preference settings.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Social Choice / Voting
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• 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

Abstract

We study committee voting rules under ranked preferences, which map the voters' preference relations to a subset of the alternatives of predefined size. In this setting, the compatibility between proportional representation and committee monotonicity is a fundamental open problem that has been mentioned in several works. We address this research question by designing a new committee voting rule called the Solid Coalition Refinement (SCR) rule that simultaneously satisfies committee monotonicity and Dummett's PSC as well as one of its variants called inclusion PSC. This is the first rule known to satisfy both of these properties. Moreover, we show that this is effectively the best that we can hope for as other fairness notions adapted from approval voting are incompatible with committee monotonicity. Finally, we prove that, for truncated preferences, the SCR rule still satisfies PSC and a property called independence of losing voter blocs, thereby refuting a conjecture of Graham-Squire et al. (2024).

Problem

• Fair Representation
• Committee Voting
• Partial Preference Information

Innovation

• Stable Coalition Refinement (SCR) rule
• Fair representation
• Partial preference compatibility