research-article

Computing the margin of victory for various voting rules

Author:

Lirong XiaAuthors Info & Claims

EC '12: Proceedings of the 13th ACM Conference on Electronic Commerce

Pages 982 - 999

https://doi.org/10.1145/2229012.2229086

Published: 04 June 2012 Publication History

Abstract

The margin of victory of an election, defined as the smallest number k such that k voters can change the winner by voting differently, is an important measurement for robustness of the election outcome. It also plays an important role in implementing efficient post-election audits, which has been widely used in the United States to detect errors or fraud caused by malfunctions of electronic voting machines.

In this paper, we investigate the computational complexity and (in)approximability of computing the margin of victory for various voting rules, including approval voting, all positional scoring rules (which include Borda, plurality, and veto), plurality with runoff, Bucklin, Copeland, maximin, STV, and ranked pairs. We also prove a dichotomy theorem, which states that for all continuous generalized scoring rules, including all voting rules studied in this paper, either with high probability the margin of victory is Θ(√n), or with high probability the margin of victory is Θ(n), where n is the number of voters. Most of our results are quite positive, suggesting that the margin of victory can be efficiently computed. This sheds some light on designing efficient post-election audits for voting rules beyond the plurality rule.

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Islam MVahidi SSchieber BBasu Roy SBaeza-Yates RBonchi F(2024)Promoting Fairness and Priority in Selecting k-Winners Using IRVProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671735(1199-1210)Online publication date: 25-Aug-2024
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Index Terms

Computing the margin of victory for various voting rules
1. Applied computing
  1. Law, social and behavioral sciences
    1. Economics
2. Computing methodologies
  1. Artificial intelligence
    1. Distributed artificial intelligence
      1. Multi-agent systems

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cover image ACM Conferences

EC '12: Proceedings of the 13th ACM Conference on Electronic Commerce

June 2012

1016 pages

ISBN:9781450314152

DOI:10.1145/2229012

General Chair:
Boi Faltings
École Polytechnique Fédérale de Lausanne (EPFL)
,
Program Chairs:
Kevin Leyton-Brown
University of British Columbia
,
Panos Ipeirotis
New York University

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 04 June 2012

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EC '12: ACM Conference on Electronic Commerce

June 4 - 8, 2012

Valencia, Spain

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Overall Acceptance Rate 664 of 2,389 submissions, 28%

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https://dl.acm.org/doi/10.24963/ijcai.2024/296
Islam MVahidi SSchieber BBasu Roy SBaeza-Yates RBonchi F(2024)Promoting Fairness and Priority in Selecting k-Winners Using IRVProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671735(1199-1210)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3671735
Williams JBaltz SStewart C(2024)Votes Can Be Confidently Bought in Some Ranked Ballot Elections, and What to Do about ItPolitical Analysis10.1017/pan.2024.4(1-13)Online publication date: 6-May-2024
https://doi.org/10.1017/pan.2024.4
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Döring MPeters JAgmon NAn BRicci AYeoh W(2023)Margin of Victory for Weighted Tournament SolutionsProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598830(1716-1724)Online publication date: 30-May-2023
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Tomlinson KUgander JKleinberg JWilliams BChen YNeville J(2023)Ballot length in instant runoff votingProceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v37i5.25724(5841-5849)Online publication date: 7-Feb-2023
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Tao LChen LXu LXu SGao ZShi W(2023)Electoral manipulation via influence: probabilistic modelAutonomous Agents and Multi-Agent Systems10.1007/s10458-023-09602-z37:1Online publication date: 8-Mar-2023
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