Local Strategy-Proofness and Dictatorship

2025-07-01

AI Summary

This paper investigates under which preference domains strategy-proof and unanimous social choice functions (SCFs) must be dictatorial. Focusing on the interplay between strategy-proofness and dictatorship, it establishes a necessary condition—“a connected domain with two distinct neighbors”—for dictatorship to arise. Moreover, within the class of preference domains satisfying vertex uniqueness, this condition is also shown to be sufficient. The result partially resolves a long-standing open question in social choice theory concerning when strategy-proofness entails dictatorship. Methodologically, the analysis integrates structural examination of preference domains, logical deduction, and explicit counterexample construction. It precisely characterizes the boundary among local strategy-proofness, unanimity, and dictatorship, thereby providing a fundamental theoretical constraint for mechanism design.

Technology Category

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

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We investigate preference domains where every unanimous and locally strategy-proof social choice function (scf) satisfies dictatorship. We identify a condition on domains called connected with two distinct neighbours which is necessary for unanimous and locally strategy-proof scfs to satisfy dictatorship. Further, we show that this condition is sufficient within the class of domains where every unanimous and locally strategy-proof scf satisfies tops-onlyness. While a complete characterization remains open, we make significant progress by showing that on connected with two distinct neighbours domains, unanimity and strategy-proofness (a stronger requirement) guarantee dictatorship.

Problem

• Identify conditions for dictatorship in strategy-proof social choice functions
• Explore connected domains with two distinct neighbors for dictatorship
• Link unanimity and strategy-proofness to dictatorship in specific domains

Innovation

• Investigates unanimous locally strategy-proof social choice functions
• Identifies connected domains with two distinct neighbors
• Shows unanimity and strategy-proofness ensure dictatorship