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Robustness of Greedy Approval Rules

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Multi-Agent Systems (EUMAS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13442))

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Abstract

We study the robustness of GreedyCC, GreedyPAV, and Phragmén’s sequential rule, using the framework introduced by Bredereck et al. [6] for the case of (multiwinner) ordinal elections and adopted to the approval setting by Gawron and Faliszewski [15]. First, we show that for each of our rules and every committee size k, there are elections in which adding or removing a certain approval causes the winning committee to completely change (i.e., the winning committee after the operation is disjoint from the one before the operation). Second, we show that the problem of deciding how many approvals need to be added (or removed) from an election to change its outcome is \({{\textrm{NP}}}\)-complete for each of our rules. Finally, we experimentally evaluate the robustness of our rules in the presence of random noise.

*See https://github.com/Project-PRAGMA/Greedy-Robust-EUMAS-2022 for the source code of the experiments performed in this paper.

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Notes

  1. 1.

    Whenever we speak of “robustness levels” without indicating whether we mean the Add or Remove variant, we collectively refer to both.

  2. 2.

    The name refers to the class of order-weighted operators (OWA operators), introduced by Yager [26] and used by Skowron et al. [22] to define a class of rules closely related to the Thiele ones.

  3. 3.

    This is mostly a technical assumption, to ensure that there are enough candidates so that all members of a committee can be replaced with non-members.

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Acknowledgments

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101002854). Grzegorz Gawron was supported in part by AGH University of Science and Technology and the “Doktorat Wdrozeniowy” program of the Polish Ministry of Science and Higher Education.

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Authors and Affiliations

  1. AGH University, Krakow, Poland

    Piotr Faliszewski, Grzegorz Gawron & Bartosz Kusek

  2. VirtusLab, Krakow, Poland

    Grzegorz Gawron

Authors
  1. Piotr Faliszewski
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  2. Grzegorz Gawron
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  3. Bartosz Kusek
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Correspondence to Piotr Faliszewski .

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Editors and Affiliations

  1. University of Düsseldorf, Düsseldorf, Germany

    Dorothea Baumeister

  2. University of Düsseldorf, Düsseldorf, Germany

    Jörg Rothe

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Faliszewski, P., Gawron, G., Kusek, B. (2022). Robustness of Greedy Approval Rules. In: Baumeister, D., Rothe, J. (eds) Multi-Agent Systems. EUMAS 2022. Lecture Notes in Computer Science(), vol 13442. Springer, Cham. https://doi.org/10.1007/978-3-031-20614-6_7

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  • DOI: https://doi.org/10.1007/978-3-031-20614-6_7

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