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Manipulation and Bribery When Aggregating Ranked Preferences

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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 and bribery have received much attention from the social choice community. We study these concepts for preference formalisms that identify a set of optimal outcomes rather than a single winning outcome. We assume that preferences may be ranked (differ in importance), and we use the Pareto principle adjusted to the case of ranked preferences as the preference aggregation rule. For two important classes of preferences, representing the extreme ends of the spectrum, we provide characterizations of situations when manipulation and bribery is possible, and establish the complexity of the problems to decide that.

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Notes

  1. 1.

    Bribery is traditionally understood as an effort by an external agent to bribe a group of voters to obtain a more satisfying result. To stress the difference between this notion and the notion we consider in the paper, we use the term simple bribery.

  2. 2.

    This method is well defined only if both sets to compare are non-empty. This is not a strong restriction because our aggregation method returns only non-empty sets of optimal outcomes.

  3. 3.

    \(a''\approx _{P/i}a'\) means \(a''\approx _{P}a'\) except for \(\succeq _{i}\).

  4. 4.

    The partition of D into strata that is determined by \(\succeq _{p}\) is not always \((D_{1},\ldots ,D_{m})\) as some sets \(D_{i}\) may be empty.

  5. 5.

    The original definition [9] allows for more general preference statements. However, they all can be effectively expressed as preference statements we defined here.

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Acknowledgments

The authors wish to thank the anonymous reviewers for useful comments and pointers to relevant literature.

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Authors and Affiliations

  1. Department of Computer Science, University of Kentucky, Lexington, KY, 40506, USA

    Ying Zhu & Miroslaw Truszczynski

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  1. Ying Zhu
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  2. Miroslaw Truszczynski
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Correspondence to Miroslaw Truszczynski .

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  1. University of New South Wales, Kensington, Australia

    Toby Walsh

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Zhu, Y., Truszczynski, M. (2015). Manipulation and Bribery When Aggregating Ranked Preferences. 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_6

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  • DOI: https://doi.org/10.1007/978-3-319-23114-3_6

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