research-article

How to Put Through Your Agenda in Collective Binary Decisions

Authors:

Robert Bredereck,

Stefan Kratsch,

Rolf Niedermeier,

Gerhard J. WoegingerAuthors Info & Claims

ACM Transactions on Economics and Computation (TEAC), Volume 4, Issue 1

Article No.: 5, Pages 1 - 28

https://doi.org/10.1145/2837467

Published: 05 January 2016 Publication History

Abstract

We consider the following decision-making scenario: a society of voters has to find an agreement on a set of proposals, and every single proposal is to be accepted or rejected. Each voter supports a certain subset of the proposals—the favorite ballot of this voter—and opposes the remaining ones. He accepts a ballot if he supports more than half of the proposals in this ballot. The task is to decide whether there exists a ballot approving a specified number of selected proposals (agenda) such that all voters (or a strict majority of them) accept this ballot.

We show that, on the negative side, both problems are NP-complete, and on the positive side, they are fixed-parameter tractable with respect to the total number of proposals or with respect to the total number of voters. We look into further natural parameters and study their influence on the computational complexity of both problems, thereby providing both tractability and intractability results. Furthermore, we provide tight combinatorial bounds on the worst-case size of an accepted ballot in terms of the number of voters.

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Cited By

Constantinescu AWattenhofer RAgmon NAn BRicci AYeoh W(2023)Computing the Best Policy that Survives a VoteProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598879(2058-2066)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598879
Chingoma JEndriss Ude Haan RPelachaud CTaylor MFaliszewski PMascardi V(2022)Simulating Multiwinner Voting Rules in Judgment AggregationProceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems10.5555/3535850.3535881(263-271)Online publication date: 9-May-2022
https://dl.acm.org/doi/10.5555/3535850.3535881

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Published In

cover image ACM Transactions on Economics and Computation

ACM Transactions on Economics and Computation Volume 4, Issue 1

December 2015

169 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/2852252

Editors:
Vincent Conitzer
Duke University
,
Preston McAfee
Google

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Copyright © 2016 ACM.

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Publication History

Published: 05 January 2016

Accepted: 01 January 2015

Revised: 01 November 2014

Received: 01 June 2014

Published in TEAC Volume 4, Issue 1

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Cited By

Constantinescu AWattenhofer RAgmon NAn BRicci AYeoh W(2023)Computing the Best Policy that Survives a VoteProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598879(2058-2066)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598879
Chingoma JEndriss Ude Haan RPelachaud CTaylor MFaliszewski PMascardi V(2022)Simulating Multiwinner Voting Rules in Judgment AggregationProceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems10.5555/3535850.3535881(263-271)Online publication date: 9-May-2022
https://dl.acm.org/doi/10.5555/3535850.3535881

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