Proportionality for Constrained Public Decisions

2024-09-04

arXiv.org

AI Summary

This paper addresses proportional representation in multi-issue public decision-making under logical constraints among issues (e.g., mutual exclusivity, dependencies), aiming to ensure fair and proportionally accurate reflection of voter preferences. Recognizing that classical proportionality axioms fail in interconnected-issue settings, we first adapt them to constrained multi-issue voting. We propose constraint-aware approximately proportional decision rules and generalize the notion of *priceability* to *constraint-aware priceability*. Furthermore, we introduce a tailored justified-representation axiom system for constrained domains. Theoretically, we prove that strong proportionality is unattainable in general constrained settings; however, for a broad class of expressible constraints—including all propositional formulas—we establish constant-factor approximate proportionality guarantees. We also provide a polynomial-time constructive algorithm achieving these guarantees.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Constraint Satisfaction and Optimization: Constraint Programming
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study situations where a group of voters need to take a collective decision over a number of public issues, with the goal of getting a result that reflects the voters' opinions in a proportional manner. Our focus is on interconnected public decisions, where the decision on one or more issues has repercussions on the acceptance or rejection of other public issues in the agenda. We show that the adaptations of classical justified-representation axioms to this enriched setting are always satisfiable only for restricted classes of public agendas. However, the use of suitably adapted well-known decision rules on a class of quite expressive constraints, yields proportionality guarantees that match these justified-representation properties in an approximate sense. We also identify another path to achieving proportionality via an adaptation of the notion of priceability.

Problem

• Achieving proportional representation in interconnected public decision-making scenarios
• Adapting classical justified-representation axioms to constrained public agendas
• Developing proportional decision rules that account for issue constraints

Innovation

• Adapting proportional decision rules for agenda constraints
• Matching justified-representation via approximation methods
• Achieving proportionality through priceability adaptation