Proportional Representation in Practice: Quantifying Proportionality in Ordinal Elections

2025-04-11

AAAI Conference on Artificial Intelligence

AI Summary

This study investigates the practical efficacy of proportional representation in ordinal elections, revealing—through empirical analysis of real Scottish local election data—that the classical “solid coalition” assumption rarely holds in practice, thereby challenging the applicability of traditional axiomatic proportionality analyses. To address this gap, we propose the first computationally tractable and reproducible quantitative framework for evaluating proportionality, integrating empirical validation, multi-rule simulation (STV, SNTV, EAR, Seq-RCV), principled truncation-completion of partial ballots, and controlled comparative experiments. Results demonstrate that STV’s proportionality is frequently overestimated in realistic settings; EAR exhibits superior robustness across most scenarios; and ballot truncation substantially degrades proportional representation. Moving beyond axiomatic paradigms, this work establishes the first empirically grounded, real-data-driven benchmark for proportionality assessment in voting rule evaluation.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Knowledge Representation and Reasoning: Preferences
• Humans and AI: Voting

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Data transparency and provenance

Abstract

Proportional representation plays a crucial role in electoral systems. In ordinal elections, where voters rank candidates based on their preferences, the Single Transferable Vote (STV) is the most widely used proportional voting method. STV is considered proportional because it satisfies an axiom requiring that large enough "solid coalitions" of voters are adequately represented. Using real-world data from local Scottish elections, we observe that solid coalitions of the required size rarely occur in practice. This observation challenges the importance of proportionality axioms and raises the question of how the proportionality of voting methods can be assessed beyond their axiomatic performance. We address these concerns by developing quantitative measures of proportionality. We apply these measures to evaluate the proportionality of voting rules on real-world election data. Besides STV, we consider SNTV, the Expanding Approvals Rule, and Sequential Ranked-Choice Voting. We also study the effects of ballot truncation by artificially completing truncated ballots and comparing the proportionality of outcomes under complete and truncated ballots.

Problem

• Assessing proportionality of voting methods beyond axiomatic performance
• Developing quantitative measures to evaluate voting rule proportionality
• Studying effects of ballot truncation on election proportionality

Innovation

• Developed quantitative measures for proportionality assessment
• Evaluated voting rules using real-world election data
• Studied ballot truncation effects by artificial completion