2022
DOI: 10.48550/arxiv.2202.06411
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How Likely A Coalition of Voters Can Influence A Large Election?

Abstract: For centuries, it has been widely believed that the influence of a small coalition of voters is negligible in a large election. Consequently, there is a large body of literature on characterizing the asymptotic likelihood for an election to be influence, especially by the manipulation of a single voter, establishing an 𝑂 ( 1 √ 𝑛) upper bound and an Ξ©( 1 𝑛 67 ) lower bound for many commonly studied voting rules under the i.i.d. uniform distribution, known as Impartial Culture (IC) in social choice, where 𝑛 … Show more

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Cited by 1 publication
(3 citation statements)
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References 50 publications
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“…This result generalizes a similar result obtained in a broad class of averagecase models by Procaccia et al [23]. It is also implied by recent work by Lirong Xia [34], though our results were obtained independently; among other results, Xia derives more precise convergence rates via more intricate techniques than we use here, but arrives at a qualitatively similar outcome. 5 Notice that when comparing formal statements, both models consider the space of histograms (vectors representing the fraction of the profile composed of each ranking) rather than profiles directly, and, while we tend to analyze the set of histograms corresponding to "bad" profiles (e.g., those in which an axiom is not satisfied) directly, Xia considers sets which are solutions to a system of linear equations and inequalities.…”
Section: Comparison Of Techniques and Resultssupporting
confidence: 92%
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“…This result generalizes a similar result obtained in a broad class of averagecase models by Procaccia et al [23]. It is also implied by recent work by Lirong Xia [34], though our results were obtained independently; among other results, Xia derives more precise convergence rates via more intricate techniques than we use here, but arrives at a qualitatively similar outcome. 5 Notice that when comparing formal statements, both models consider the space of histograms (vectors representing the fraction of the profile composed of each ranking) rather than profiles directly, and, while we tend to analyze the set of histograms corresponding to "bad" profiles (e.g., those in which an axiom is not satisfied) directly, Xia considers sets which are solutions to a system of linear equations and inequalities.…”
Section: Comparison Of Techniques and Resultssupporting
confidence: 92%
“…Novel results include smoothed analysis of Arrow's theorem and analyses of the axioms Consistency and Independence of Irrelevant Alternatives. In independent work from Xia's recent paper [34], we also show the smoothed-satisfaction of coalition-based notions of Strategy-Proofness, Monotonocity, and Participation. A final, central component of our contributions are the high-level insights and future directions we identify based on this work, which we describe in detail to maximally facilitate additional research in this area.…”
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confidence: 91%
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