The Impossibility of Strategyproof Rank Aggregation

2026-02-06

AI Summary

This study investigates whether a social welfare function (SWF) for preference aggregation can simultaneously satisfy anonymity, consistency, and strategyproofness. By integrating SAT-based automated theorem proving, interactive formal verification in Isabelle, and manual mathematical reasoning, the authors present the first computer-assisted proof establishing that no such SWF exists when there are at least four alternatives. This result reveals a fundamental incompatibility between strategyproofness and basic fairness axioms. Furthermore, it demonstrates that two natural classes of SWFs are highly manipulable, exhibiting substantial incentive ratios, thereby underscoring the general incompatibility between majority consistency and strategyproofness in social choice settings.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Data transparency and provenance

Abstract

In rank aggregation, the goal is to combine multiple input rankings into a single output ranking. In this paper, we analyze rank aggregation methods, so-called social welfare functions (SWFs), with respect to strategyproofness, which requires that no agent can misreport his ranking to obtain an output ranking that is closer to his true ranking in terms of the Kemeny distance. As our main result, we show that no anonymous SWF satisfies unanimity and strategyproofness when there are at least four alternatives. This result is proven by SAT solving, a computer-aided theorem proving technique, and verified by Isabelle, a highly trustworthy interactive proof assistant. Further, we prove by hand that strategyproofness is incompatible with majority consistency, a variant of Condorcet-consistency for SWFs. Lastly, we show that all SWFs in two natural classes have a large incentive ratio and are thus highly manipulable.

Problem

• rank aggregation
• strategyproofness
• social welfare functions
• Kemeny distance
• manipulability

Innovation

• strategyproofness
• rank aggregation
• SAT solving
• formal verification
• social welfare functions