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Complexity of Manipulative Actions When Voting with Ties

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Book cover Algorithmic Decision Theory (ADT 2015)

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

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Abstract

Most of the computational study of election problems has assumed that each voter’s preferences are, or should be extended to, a total order. However in practice voters may have preferences with ties. We study the complexity of manipulative actions on elections where voters can have ties, extending the definitions of the election systems (when necessary) to handle voters with ties. We show that for natural election systems allowing ties can both increase and decrease the complexity of manipulation and bribery, and we state a general result on the effect of voters with ties on the complexity of control.

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Notes

  1. 1.

    Here and elsewhere we write \(\sum \!A\) to denote \(\sum _{a \in A} a\).

  2. 2.

    A similar situation occurred in the proof of Proposition 5 in Narodytska and Walsh [25], where a (very different) specialized version of Subset Sum was constructed to prove that 3-candidate Borda CWCM (in the non-single-peaked case) for top orders using average remained NP-complete.

  3. 3.

    By triviality we mean a scoring rule with a scoring vector that gives each candidate the same score.

  4. 4.

    Menon and Larson independently proved the top order case of the following theorem [24].

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Acknowledgments

The authors thank Aditi Bhatt, Kimaya Kamat, Matthew Le, David Narváez, Amol Patil, Ashpak Shaikh, and the anonymous referees for their helpful comments. This work was supported in part by NSF grant no. CCF-1101452 and a National Science Foundation Graduate Research Fellowship under NSF grant no. DGE-1102937.

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Authors and Affiliations

  1. College of Computing and Information Sciences, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Zack Fitzsimmons

  2. Department of Computer Science, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Edith Hemaspaandra

Authors
  1. Zack Fitzsimmons
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  2. Edith Hemaspaandra
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Correspondence to Zack Fitzsimmons .

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Editors and Affiliations

  1. University of New South Wales, Kensington, Australia

    Toby Walsh

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Fitzsimmons, Z., Hemaspaandra, E. (2015). Complexity of Manipulative Actions When Voting with Ties. 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_7

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  • DOI: https://doi.org/10.1007/978-3-319-23114-3_7

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-23114-3

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