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Robustness of Approval-Based Multiwinner Voting Rules

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Algorithmic Decision Theory (ADT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11834))

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Abstract

We investigate how robust are approval-based multiwinner voting rules to small perturbations of the preference profiles. In particular, we consider the extent to which a committee can change after we add/remove/swap one approval, and we consider the computational complexity of deciding how many such operations are necessary to change the set of winning committees. We also consider the counting variants of our problems, which can be interpreted as computing the probability that the result of an election changes after a given number of random perturbations of the preference profile.

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Notes

  1. 1.

    The class \({{\mathrm {FP}}}\) contains polynomial-time computable functions and the class \({{\mathrm {\#P}}}\) is the analogue of \({{\mathrm {NP}}}\) for counting problems.

  2. 2.

    Since it is easy to compute the total number of ways of performing B operations of a given type, from the computational complexity point of view it is irrelevant if we count the cases where the result changes or does not change , but the latter approach simplifies our proofs.

  3. 3.

    We assume that it is, indeed, possible to add B approvals, i.e., \(z_1 + \cdots + z_m \le nm-B\).

  4. 4.

    For each \(u \in [n]\), we take \(f(n+1,u)\) to be equal to f(n, u) in this formula.

  5. 5.

    From the previous case we know that it is possible to increase the score of this vertex candidate to the original value by adding some approval for him or her.

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Acknowledgements

This work was partially supported by the AGH University and the “Doktorat Wdrozeniowy” program of the Polish Ministry of Science and Higher Education.

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Authors and Affiliations

  1. VirtusLab, Krakow, Poland

    Grzegorz Gawron

  2. AGH University, Krakow, Poland

    Grzegorz Gawron & Piotr Faliszewski

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  1. Grzegorz Gawron
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  2. Piotr Faliszewski
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Correspondence to Piotr Faliszewski .

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Editors and Affiliations

  1. Fuqua School of Business, Duke University, Durham, NC, USA

    Saša Pekeč

  2. Florida Institute for Human and Machine Cognition (IHMC), Pensacola, FL, USA

    Kristen Brent Venable

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Gawron, G., Faliszewski, P. (2019). Robustness of Approval-Based Multiwinner Voting Rules. In: Pekeč, S., Venable, K.B. (eds) Algorithmic Decision Theory. ADT 2019. Lecture Notes in Computer Science(), vol 11834. Springer, Cham. https://doi.org/10.1007/978-3-030-31489-7_2

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  • DOI: https://doi.org/10.1007/978-3-030-31489-7_2

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