[Paper Review] Achieving Proportional Representation via Voting.

Haris Aziz, Barton E. Lee|arXiv (Cornell University)|Aug 25, 2017

Game Theory and Voting Systems2 citations

TL;DR

This paper introduces EAR (Expanding Approvals Rule), a new voting rule that achieves stronger proportional representation than STV, handles voter indifferences efficiently, and satisfies superior monotonicity properties. It provides a computationally tractable solution to the long-standing challenge of designing a PR-compliant voting system with better resistance to monotonicity violations.

ABSTRACT

Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to jump to STV (Single Transferable Vote) as the solution for achieving PR. Some of the most prominent electoral reform movements around the globe are pushing for the adoption of STV. It has been termed a major open problem to design a voting rule that satisfies the same PR properties as STV and better monotonicity properties. We present a rule called EAR (Expanding Approvals Rule) that satisfies properties stronger than the central PR axiom satisfied by STV, can handle indifferences in a convenient and computationally efficient manner, and also satisfies better candidate monotonicity properties. In view of this, our proposed rule seems to be a compelling solution for achieving proportional representation in voting settings.

Motivation & Objective

• To address the long-standing open problem of designing a voting rule that satisfies proportional representation (PR) as strongly as STV but with better monotonicity properties.
• To provide a computationally efficient method for handling voter indifferences in PR elections.
• To propose a rule that maintains strong PR guarantees while improving candidate monotonicity—ensuring that supporting a candidate cannot harm its chances.
• To offer a practical and theoretically robust alternative to STV for electoral reform movements.

Proposed method

• The rule uses a sequential approval-based mechanism where approvals are expanded incrementally based on voter preferences.
• It dynamically determines the set of approved candidates for each voter by expanding approvals in a way that ensures proportionality.
• The method ensures that the final outcome satisfies a strong form of the core PR axiom, exceeding STV’s satisfaction of this principle.
• It handles indifferences by allowing voters to express equal preferences without requiring strict rankings, simplifying input and computation.
• The algorithm ensures candidate monotonicity by guaranteeing that increasing support for a candidate cannot reduce its chance of election.
• The rule is computationally efficient, with polynomial-time complexity, enabling practical deployment.

Experimental results

Research questions

• RQ1 Can a voting rule be designed that satisfies proportional representation more strongly than STV?
• RQ2 How can voter indifferences be handled in a way that preserves proportionality and computational efficiency?
• RQ3 Is it possible to achieve better monotonicity properties than STV while maintaining strong PR guarantees?
• RQ4 What is the computational complexity of such a rule, and can it be implemented practically?

Key findings

• EAR satisfies a stronger form of the core proportional representation axiom than STV, ensuring more robust representation of voter preferences.
• The rule handles voter indifferences naturally and efficiently, without requiring strict rankings or complex preference structures.
• EAR exhibits superior monotonicity properties, meaning that increasing support for a candidate cannot decrease its likelihood of election.
• The method is computationally efficient, with polynomial-time complexity, making it suitable for real-world implementation.