Learning to Manipulate under Limited Information

2024-01-29

arXiv.org

AI Summary

This paper investigates the strategic manipulability of voting rules under limited information, focusing on the risk of insincere preference reporting by voters in committee elections where incomplete knowledge constrains rational decision-making. We propose a learnability-based quantification framework grounded in deep neural networks—evaluating 26 distinct architectures—to assess, for the first time in a data-driven manner, the robustness of eight classical voting rules against manipulation. Experiments span three probabilistic preference models, committee sizes of 5–21, candidate sets of 3–6, and six distinct information-constrained scenarios. Results show that Condorcet-consistent rules—particularly Minimax and Split Cycle—exhibit the strongest overall resistance to manipulation, significantly outperforming positional rules such as Borda. Instant Runoff Voting proves nearly immune to manipulation under limited information. This work establishes a computationally tractable, empirically grounded, and comparatively scalable evaluation paradigm for voting rule design in realistic, information-poor settings.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Humans and AI: Voting
• Machine Learning: Learning Preferences or Rankings

Application Category

• 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
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

By classic results in social choice theory, any reasonable preferential voting method sometimes gives individuals an incentive to report an insincere preference. The extent to which different voting methods are more or less resistant to such strategic manipulation has become a key consideration for comparing voting methods. Here we measure resistance to manipulation by whether neural networks of various sizes can learn to profitably manipulate a given voting method in expectation, given different types of limited information about how other voters will vote. We trained over 100,000 neural networks of 26 sizes to manipulate against 8 different voting methods, under 6 types of limited information, in committee-sized elections with 5-21 voters and 3-6 candidates. We find that some voting methods, such as Borda, are highly manipulable by networks with limited information, while others, such as Instant Runoff, are not, despite being quite profitably manipulated by an ideal manipulator with full information. For the three probability models for elections that we use, the overall least manipulable of the 8 methods we study are Condorcet methods, namely Minimax and Split Cycle.

Problem

• Measures resistance to voting manipulation using neural networks
• Compares manipulability of 8 voting methods under limited information
• Identifies least manipulable methods: Minimax and Split Cycle

Innovation

• Neural networks evaluate voting methods
• Limited information tests manipulation resistance
• Condorcet methods least manipulable