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The Complexity of Voter Control and Shift Bribery Under Parliament Choosing Rules

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Transactions on Computational Collective Intelligence XXIII

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 9760))

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Abstract

We study the complexity of voter control and shift bribery problems under two parliament choosing rules, one based on the Plurality rule and one based on the Borda rule (considering both the case where there is a threshold a party needs to pass to enter the parliament, and the case where there is no such threshold). A parliament choosing rule is a function that given a preference profile of the voters (where each voter ranks political parties) outputs the fraction of seats each of the parties should receive in the parliament. We study the complexity of three problems, shift bribery, control by adding voters, and control by deleting voters, where some agent modifies the election in order to increase the fraction of the seats in parliament assigned to a given party. We show that in most cases these problems can be solved in polynomial time for our parliament choosing rules, but we also show several \({{\mathrm {NP}}}\)-hardness results (for the Borda-based rule, for the case where there is a threshold for entering the parliament).

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Notes

  1. 1.

    One may say that we should add exactly \(k'\) votes. However, certainly if we add fewer than \(k'\) votes but c will have score at least \(G_{\min }\), c will receive at least g fraction of seats in the parliament.

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Acknowledgments

The authors are very grateful to the reviewers for helpful comments. Piotr Faliszewski was supported by NCN grant DEC-2012/06/M/ST1/00358.

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Authors and Affiliations

  1. AGH University, Krakow, Poland

    Tomasz Put & Piotr Faliszewski

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  1. Tomasz Put
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  2. Piotr Faliszewski
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Correspondence to Piotr Faliszewski .

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Editors and Affiliations

  1. Wrocław University of Technology, Wrocław, Poland

    Ngoc Thanh Nguyen

  2. Swinburne University of Technology, Hawthorn, Australia

    Ryszard Kowalczyk

  3. WSB University in Wroclaw, Wroclaw, Poland

    Jacek Mercik

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Put, T., Faliszewski, P. (2016). The Complexity of Voter Control and Shift Bribery Under Parliament Choosing Rules. In: Nguyen, N., Kowalczyk, R., Mercik, J. (eds) Transactions on Computational Collective Intelligence XXIII. Lecture Notes in Computer Science(), vol 9760. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52886-0_3

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  • DOI: https://doi.org/10.1007/978-3-662-52886-0_3

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