research-article

Equilibria of plurality voting with abstentions

Authors:

Edith ElkindAuthors Info & Claims

EC '10: Proceedings of the 11th ACM conference on Electronic commerce

Pages 347 - 356

https://doi.org/10.1145/1807342.1807398

Published: 07 June 2010 Publication History

Abstract

In the traditional voting manipulation literature, it is assumed that a group of manipulators jointly misrepresent their preferences to get a certain candidate elected, while the remaining voters are truthful. In this paper, we depart from this assumption, and consider the setting where all voters are strategic. In this case, the election can be viewed as a game, and the election outcomes correspond to Nash equilibria of this game. We use this framework to analyze two variants of Plurality voting, namely, simultaneous voting, where all voters submit their ballots at the same time, and sequential voting, where the voters express their preferences one by one. For simultaneous voting, we characterize the preference profiles that admit a pure Nash equilibrium, but show that it is computationally hard to check if a given profile fits our criterion. For sequential voting, we provide a complete analysis of the setting with two candidates, and show that for three or more candidates the equilibria of sequential voting may behave in a counterintuitive manner.

References

[1]

M. Battaglini. Sequential Voting with Abstention, Game Econ. Behav. 51, pp. 445--463, 2005.

[2]

T. Borgers. Costly Voting, Am. Econ. Rev. 94:1, pp. 57--66, 2004.

[3]

S. Callander. Bandwagons and Momentum in Sequential Voting, Rev. Econ. Stud. 74, pp. 653--684, 2007.

[4]

E. Dekel, M. Piccione. Sequential Voting Procedures in Symmetric Binary Elections, J. Polit. Econ. 108:1, pp. 34--55, 2000.

[5]

A. Dhillon, B. Lockwood. When are Plurality Rule Voting Games Dominance-solvable?, Game Econ. Behav. 46, pp. 55--75, 2004.

[6]

Y. Desmedt, E. Elkind. Equilibria of Plurality Voting with Abstentions, available from http://arxiv.org/abs/1001.4939.

Digital Library

[7]

U. Endriss, P. Goldberg, editors. Proc. COMSOC-08, 2008.

[8]

E. Ephrati and J. Rosenschein. A Heuristic Technique for Multi-agent Planning, Annals of Mathematics and Artificial Intelligence, 20(1-4), pp. 13--67, 1997.

Digital Library

[9]

R. Farquharson. Theory of Voting, Yale University Press, 1969.

[10]

M. Fey. Informational Cascades and Sequential Voting, working paper, 2000.

[11]

A. F. Gibbard. Manipulation of Voting Schemes: a General Result, Econometrica, 41, pp 597--601, 1973.

[12]

A. Mas-Colell, M. Whinston, and J. R. Green. Microeconomic Theory, Oxford University Press, 1995.

[13]

R. B. Morton, K. C. Williams. Information Asymmetries and Simultaneous versus Sequential Voting, Am. Polit. Sci. Rev. 93:1, pp. 51--67, 1999.

[14]

H. Moulin. Dominance Solvable Voting Schemes, Econometrica, 47:1337--1351, 1979.

[15]

R. Myerson, R. Weber, A Theory of Voting Equilibria, Am. Polit. Sci. Rev. 87:1, pp. 102--114, 1993.

[16]

J. Nash. Equilibrium Points in n-person Games, Proc. Natl. Acad. of Sci. 36, pp. 48--49, 1950.

[17]

N. Persico, Committee Design with Endogenous Information, Rev. Econ. Stud. 70, pp.1--27, 2003.

[18]

M. A. Satterthwaite. Strategy-proofness and Arrow's Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions, J. Econ. Theory, 10, pp. 187--217, 1975.

[19]

R. Selten. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, Int. J. Game Theory 4:1, pp. 25-55, 1975.

Digital Library

[20]

F. De Sinopoli. Sophisticated Voting and Equilibrium Refinements Under Plurality Rule, Soc. Choice Welfare 17:4, pp. 655--672, 2000.

[21]

F. De Sinopoli, G. Iannantuoni. On the Generic Strategic Stability of Nash Equilibria if Voting is Costly, Econ. Theory 25:2, pp. 477--486, 2005.

[22]

B. Sloth. The Theory of Voting and Equilibria in Noncooperative Games, Game Econ. Behav. 5:1, pp. 152--169, 1993.

[23]

L. Xia, V. Conitzer. Stackelberg Voting Games: Computational Aspects and Paradoxes, to appear in AAAI-10, 2010.

Cited By

Terzopoulou ZTerzopoulos PEndriss U(2024)Iterative Voting with Partial PreferencesArtificial Intelligence10.1016/j.artint.2024.104133(104133)Online publication date: Apr-2024
https://doi.org/10.1016/j.artint.2024.104133
Kavner JMeir RRossi FXia LElkind E(2023)Convergence of multi-issue iterative voting under uncertaintyProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/310(2783-2791)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/310
Müller MPuppe C(2023)Strategy-proofness implies minimal participation under single-peakednessEconomic Theory Bulletin10.1007/s40505-023-00247-511:1(131-151)Online publication date: 25-Apr-2023
https://doi.org/10.1007/s40505-023-00247-5
Show More Cited By

Index Terms

Equilibria of plurality voting with abstentions
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

Recommendations

Sequential voting with externalities: herding in social networks
EC '12: Proceedings of the 13th ACM Conference on Electronic Commerce

We study sequential voting with two alternatives, in a setting with utility externalities: as usual, each voter has a private preference over the candidates and likes her favorite candidate to win, but additionally, a voter values voting for the chosen ...
Trembling hand equilibria of plurality voting
IJCAI'16: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence

Trembling hand (TH) equilibria were introduced by Selten in 1975. Intuitively, these are Nash equilibria that remain stable when players assume that there is a small probability that other players will choose off-equilibrium strategies. This concept is ...
Complexity of Finding Equilibria of Plurality Voting Under Structured Preferences
AAMAS '16: Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems

We study the complexity of finding pure Nash equilibria in voting games over well-known restricted preference domains, such as the domains of single-peaked and single-crossing preferences. We focus on the Plurality rule, and, following the recent work ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

EC '10: Proceedings of the 11th ACM conference on Electronic commerce

June 2010

400 pages

ISBN:9781605588223

DOI:10.1145/1807342

General Chair:
David C. Parkes
Harvard University, USA
,
Program Chairs:
Chrysanthos Dellarocas
Boston University, USA
,
Moshe Tennenholtz
Technion and Microsoft Israel R&D Center

Copyright © 2010 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]

Sponsors

SIGecom: Special Interest Group on Economics and Computation

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 07 June 2010

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

EC '10

Sponsor:

SIGecom

EC '10: ACM Conference on Electronic Commerce

June 7 - 11, 2010

Massachusetts, Cambridge, USA

Acceptance Rates

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

Upcoming Conference

EC '25

Sponsor:
sigecom

The 25th ACM Conference on Economics and Computation

July 7 - 11, 2025

Stanford , CA , USA

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

46
Total Citations
View Citations
279
Total Downloads

Downloads (Last 12 months)27
Downloads (Last 6 weeks)0

Reflects downloads up to 25 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Terzopoulou ZTerzopoulos PEndriss U(2024)Iterative Voting with Partial PreferencesArtificial Intelligence10.1016/j.artint.2024.104133(104133)Online publication date: Apr-2024
https://doi.org/10.1016/j.artint.2024.104133
Kavner JMeir RRossi FXia LElkind E(2023)Convergence of multi-issue iterative voting under uncertaintyProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/310(2783-2791)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/310
Müller MPuppe C(2023)Strategy-proofness implies minimal participation under single-peakednessEconomic Theory Bulletin10.1007/s40505-023-00247-511:1(131-151)Online publication date: 25-Apr-2023
https://doi.org/10.1007/s40505-023-00247-5
Hemaspaandra EHemaspaandra LRothe J(2022)The complexity of online bribery in sequential electionsJournal of Computer and System Sciences10.1016/j.jcss.2022.01.006127(66-90)Online publication date: Aug-2022
https://doi.org/10.1016/j.jcss.2022.01.006
Bielous GMeir R(2022)Proxy Manipulation for Better OutcomesMulti-Agent Systems10.1007/978-3-031-20614-6_5(79-95)Online publication date: 11-Dec-2022
https://doi.org/10.1007/978-3-031-20614-6_5
Meir RTalmon NShahaf GShapiro E(2022)Sybil-Resilient Social Choice with Low Voter TurnoutMulti-Agent Systems10.1007/978-3-031-20614-6_15(257-274)Online publication date: 11-Dec-2022
https://doi.org/10.1007/978-3-031-20614-6_15
Anthony BMedina AMueller M(2022)Prioritizing Self, Team, or Job: Trends in Sincerity in Cooperative PollsCooperative Design, Visualization, and Engineering10.1007/978-3-031-16538-2_4(33-44)Online publication date: 25-Oct-2022
https://dl.acm.org/doi/10.1007/978-3-031-16538-2_4
Kavner JXia LRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)Strategic behavior is blissProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3541715(19021-19032)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.5555/3540261.3541715
Seddighin MLatifian MGhodsi M(2021)On the Distortion Value of Elections with AbstentionJournal of Artificial Intelligence Research10.1613/jair.1.1230670(567-595)Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1613/jair.1.12306
Elkind EGrandi URossi FSlinko A(2020) Cognitive hierarchy and voting manipulation in -approval voting Mathematical Social Sciences10.1016/j.mathsocsci.2020.07.001Online publication date: Jul-2020
https://doi.org/10.1016/j.mathsocsci.2020.07.001
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten