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Complexity of Bribery and Control for Uniform Premise-Based Quota Rules Under Various Preference Types

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Algorithmic Decision Theory (ADT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9346))

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Abstract

Manipulation of judgment aggregation procedures has first been studied by List [14] and Dietrich and List [8], and Endriss et al. [9] were the first to study it from a computational perspective. Baumeister et al. [2, 3, 6] introduced the concepts of bribery and control in judgment aggregation and studied their algorithmic and complexity-theoretic properties. However, their results are restricted to Hamming-distance-respecting preferences and their results on bribery apply to the premise-based procedure only. We extend these results to more general preference notions, including closeness-respecting and top-respecting preferences that are due to Dietrich and List and have been applied to manipulation in judgment aggregation by Baumeister et al. [4, 5]. In addition, our results apply to uniform premise-based quota rules that generalize the premise-based procedure.

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Notes

  1. 1.

    There are also irresolute judgment aggregation procedures (i.e., procedures that may output more than one collective judgment set), such as the distance-based procedures introduced by Pigozzi [17] and Miller and Osherson [15], which we won’t consider here, though.

  2. 2.

    This result is shown for the quota only.

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Acknowledgments

We thank the anonymous reviewers for their helpful comments. This work was supported in part by a grant for gender-sensitive universities from the NRW Ministry for Innovation, Science, and Research and by DFG grant RO 1202/15-1.

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Authors and Affiliations

  1. Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, 40225, Düsseldorf, Germany

    Dorothea Baumeister, Jörg Rothe & Ann-Kathrin Selker

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  1. Dorothea Baumeister
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  2. Jörg Rothe
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  3. Ann-Kathrin Selker
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Correspondence to Ann-Kathrin Selker .

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  1. University of New South Wales, Kensington, Australia

    Toby Walsh

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Baumeister, D., Rothe, J., Selker, AK. (2015). Complexity of Bribery and Control for Uniform Premise-Based Quota Rules Under Various Preference Types. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_26

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  • DOI: https://doi.org/10.1007/978-3-319-23114-3_26

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