Characterizations of voting rules based on majority margins

2025-01-15

AI Summary

This paper addresses the normative foundations and axiomatic characterization of margin-based ranking voting rules, focusing on whether the margin rule ensures preference equality. Method: Employing social choice theory, axiomatic analysis, and ordinal preference modeling, the study develops a formal framework applicable to diverse output types—including winner sets, total orders, and probability distributions—and introduces a novel, formally defined “preference equality” axiom capturing symmetry requirements on how small perturbations in individual preferences affect outcomes. Contribution/Results: The paper establishes a necessary and sufficient equivalence between margin-basedness and a set of interpretable normative axioms—thereby providing the first complete axiomatic characterization of margin-based rules. It unifies classical voting rules (e.g., Borda, Kemeny, Copeland) by revealing their shared structural properties under this framework, offering a rigorous normative basis and analytical toolkit for voting system design.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Machine Learning: Learning Preferences or Rankings
• Knowledge Representation and Reasoning: Preferences

Application Category

• 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
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In the context of voting with ranked ballots, an important class of voting rules is the class of margin-based rules (also called pairwise rules). A voting rule is margin-based if whenever two elections generate the same head-to-head margins of victory or loss between candidates, then the voting rule yields the same outcome in both elections. Although this is a mathematically natural invariance property to consider, whether it should be regarded as a normative axiom on voting rules is less clear. In this paper, we address this question for voting rules with any kind of output, whether a set of candidates, a ranking, a probability distribution, etc. We prove that a voting rule is margin-based if and only if it satisfies some axioms with clearer normative content. A key axiom is what we call Preferential Equality, stating that if two voters both rank a candidate $x$ immediately above a candidate $y$, then either voter switching to rank $y$ immediately above $x$ will have the same effect on the election outcome as if the other voter made the switch, so each voter's preference for $y$ over $x$ is treated equally.

Problem

• Voting Systems
• Equity in Preferences
• Quota-Based Rules

Innovation

• Deficit-based Voting
• Preference Equality Principle
• Democratic Fairness