Robust Voting Rules on the Interval Domain

2025-09-05

AI Summary

This paper investigates the robustness of voting rules under interval preferences, where voters report ordered intervals representing their support over a totally ordered set of candidates. We introduce the class of *position-threshold rules*, axiomatically characterized by reinforcement and a novel robustness axiom—*robustness to interval perturbations*—thereby pioneering the formal integration of robustness into social choice theory for interval-valued preferences. Our characterization yields necessary and sufficient conditions for this rule class and naturally generalizes the classical median rule: its outcome corresponds to a robust central location of the collective support intervals. Methodologically, we combine sequential preference modeling with axiomatic analysis, providing both a theoretical foundation and a computationally tractable framework for collective decision-making under fuzziness and interval uncertainty.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Reasoning under Uncertainty: Decision/Utility Theory
• Knowledge Representation and Reasoning: Preferences

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

In this paper, we study voting rules on the interval domain, where the alternatives are arranged according to an externally given strict total order and voters report intervals of this order to indicate the alternatives they support. For this setting, we introduce and characterize the class of position-threshold rules, which compute a collective position of the voters with respect to every alternative and choose the left-most alternative whose collective position exceeds its threshold value. Our characterization of these rules mainly relies on reinforcement, a well-known population consistency condition, and robustness, a new axiom that restricts how the outcome is allowed to change when a voter removes the left-most or right-most alternative from his interval. Moreover, we characterize a generalization of the median rule to the interval domain, which selects the median of the endpoints of the voters' intervals.

Problem

• Characterizing position-threshold rules for interval voting domains
• Introducing robustness axiom for interval endpoint modifications
• Generalizing median rule to interval-based preference aggregation

Innovation

• Position-threshold rules for interval voting
• Reinforcement and robustness axioms characterization
• Generalized median rule for interval endpoints