How Many Votes is a Lie Worth? Measuring Strategyproofness through Resource Augmentation

2026-02-26

AI Summary

This study investigates the intensity of incentives for strategic voting—defined as the gain a voter can achieve by misrepresenting their preferences—under different voting rules. To this end, the authors propose a “resource augmentation” framework that introduces a novel measure based on the number of replicated voters, enabling a systematic quantification and comparison of the manipulability of various social choice functions. Theoretical analysis reveals that when the number of candidates is smaller than the number of voters, the Borda Count exhibits the lowest manipulability; otherwise, Plurality is least manipulable. Moreover, no Condorcet-consistent rule outperforms Plurality in terms of resistance to manipulation, and the Borda Count is uniquely characterized by manipulability that does not increase with the electorate size. This work is the first to unify positional scoring rules and Condorcet methods within a single framework, uncovering fundamental differences in their strategic robustness.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Humans and AI: Voting
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

It is well known, by the Gibbard-Satterthwaite Theorem, that when there are more than two candidates, any non-dictatorial voting rule can be manipulated by untruthful voters. But how strong is the incentive to manipulate under different voting rules? We suggest measuring the potential advantage of a strategic voter by asking how many copies of their (truthful) vote must be added to the election in order to achieve an outcome as good as their best manipulation. Intuitively, this definition quantifies what a voter can gain by manipulating in comparison to what they would have gained by finding like-minded voters to join the election. The higher the former is, the more incentive a voter will have to manipulate, even when it is computationally costly. Using this framework, we obtain a principled method to measure and compare the manipulation potential for different voting rules. We analyze and report this potential for well-known and broad classes of social choice functions. In particular, we show that the positional scoring rule with the smallest manipulation potential will always be either Borda Count (if the number of voters outweighs the number of candidates) or Plurality (vice versa). Further, we prove that any rule satisfying a weak form of majority consistency (and therefore any Condorcet-consistent rule) cannot outperform Plurality, and that any majoritarian Condorcet rule will perform significantly worse. Consequently, out of the voting rules we analyze, Borda Count stands out as the only one with a manipulation potential that does not grow with the number of voters. By establishing a clear separation between different rules in terms of manipulation potential, our work paves the way for the search for rules that provide voters with minimal incentive to manipulate.

Problem

• strategyproofness
• voting rules
• manipulation incentive
• Gibbard-Satterthwaite Theorem
• social choice

Innovation

• strategyproofness
• resource augmentation
• voting rules
• manipulation potential
• Borda Count