How Many Votes is a Lie Worth? Measuring Strategyproofness through Resource Augmentation
Ratip Emin Berker, Vincent Conitzer, Eden Hartman, Jiayuan Liu, and Caspar Oesterheld

TL;DR
This paper introduces a novel resource augmentation framework to measure the strength of manipulation incentives in voting rules, revealing fundamental differences among popular social choice functions.
Contribution
It proposes a new method to quantify manipulation potential via resource augmentation and analyzes various voting rules, highlighting Borda Count's minimal manipulation incentive.
Findings
Borda Count has the lowest manipulation potential among analyzed rules.
Majoritarian Condorcet rules perform worse in terms of manipulation potential.
Manipulation potential for Borda Count does not grow with the number of voters.
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…
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Taxonomy
TopicsGame Theory and Voting Systems · Benford’s Law and Fraud Detection · Electoral Systems and Political Participation
