research-article

Manipulating two stage voting rules

Authors:

Nina Narodytska,

Toby WalshAuthors Info & Claims

AAMAS '13: Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems

Pages 423 - 430

Published: 06 May 2013 Publication History

Abstract

We study the computational complexity of computing a manipulation of a two stage voting rule. An example of a two stage voting rule is Black's procedure. The first stage of Black's procedure selects the Condorcet winner if it exists, otherwise the second stage selects the Borda winner. In general, we argue that there is no connection between the computational complexity of manipulating the two stages of such a voting rule and that of the whole. However, we also demonstrate that we can increase the complexity of even a very simple base rule by adding a simple first stage to the front of the base rule. In particular, whilst Plurality is polynomial to manipulate, we show that the two stage rule that selects the Condorcet winner if it exists and otherwise computes the Plurality winner is NP-hard to manipulate with three or more candidates, weighted votes and a coalition of manipulators. In fact, with any scoring rule, computing a coalition manipulation of the two stage rule that selects the Condorcet winner if they exist and otherwise applies the scoring rule is NP-hard with three or more candidates and weighted votes. It follows that computing a coalition manipulation of Black's procedure is NP-hard with weighted votes. With unweighted votes, we prove that the complexity of manipulating Black's procedure is inherited from the Borda rule that it includes. More specifically, a single manipulator can compute a manipulation of Black's procedure in polynomial time, but computing a manipulation is NP-hard for two manipulators. With two stage voting rules, we can also allow agents to re-vote between rounds. We study the impact of such re-voting on manipulation.

References

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Cited By

Fitzsimmons ZHemaspaandra EHemaspaandra L(2016)Manipulation Complexity of Same-System Runoff ElectionsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-015-9490-677:3-4(159-189)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1007/s10472-015-9490-6
Dey PMisra NNarahari YWeiss GYolum PBordini RElkind E(2015)Detecting Possible Manipulators in ElectionsProceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems10.5555/2772879.2773336(1441-1450)Online publication date: 4-May-2015
https://dl.acm.org/doi/10.5555/2772879.2773336

Index Terms

Manipulating two stage voting rules
1. Computing methodologies
  1. Artificial intelligence
    1. Distributed artificial intelligence
      1. Multi-agent systems

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Published In

cover image ACM Other conferences

AAMAS '13: Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems

May 2013

1500 pages

ISBN:9781450319935

General Chairs:
Maria Gini
University of Minnesota, USA
,
Onn Shehory
IBM Haifa Research Lab, Israel
,
Program Chairs:
Takayuki Ito
Nagoya Institute of Technology, Japan
,
Catholijn Jonker
Delft Institute of Technology, The Netherlands

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IFAAMAS

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SIGAI: ACM Special Interest Group on Artificial Intelligence

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International Foundation for Autonomous Agents and Multiagent Systems

Richland, SC

Publication History

Published: 06 May 2013

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AAMAS '13

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AAMAS '13: International conference on Autonomous Agents and Multi-Agent Systems

May 6 - 10, 2013

MN, St. Paul, USA

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AAMAS '13 Paper Acceptance Rate 140 of 599 submissions, 23%;

Overall Acceptance Rate 1,155 of 5,036 submissions, 23%

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Cited By

Fitzsimmons ZHemaspaandra EHemaspaandra L(2016)Manipulation Complexity of Same-System Runoff ElectionsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-015-9490-677:3-4(159-189)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1007/s10472-015-9490-6
Dey PMisra NNarahari YWeiss GYolum PBordini RElkind E(2015)Detecting Possible Manipulators in ElectionsProceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems10.5555/2772879.2773336(1441-1450)Online publication date: 4-May-2015
https://dl.acm.org/doi/10.5555/2772879.2773336

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