Complexity of control by partitioning veto elections and of control by adding candidates to plurality elections

Abstract

Control by partition refers to situations where an election chair seeks to influence the outcome of an election by partitioning either the candidates or the voters into two groups, thus creating two first-round subelections that determine who will take part in a final round. The model of partition-of-voters control attacks is remotely related to “gerrymandering” (maliciously resizing election districts). While the complexity of control by partition has been studied thoroughly for many voting systems, there are no such results known for the important veto voting system. We settle the complexity of control by partition for veto in a broad variety of models. In addition, by giving a counterexample we observe that a reduction from the literature (Chen et al. 2015) showing the parameterized complexity of control by adding candidates to plurality elections, parameterized by the number of voters, is technically flawed, and we show how this reduction can be adapted to make it correct.

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Acknowledgements

We thank the AMAI, AAMAS-2017, ECAI-2016, and ISAIM-2016 reviewers for many helpful suggestions. This work has been supported in part by DFG grant RO-1202/15-1.

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Correspondence to Cynthia Maushagen.

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Preliminary versions of this paper have been presented at the 14th International Symposium on Artificial Intelligence and Mathematics (ISAIM 2016) and have appeared in the proceedings of the 22nd European Conference on Artificial Intelligence (ECAI 2016) [33] and of the 16th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2017) [34]. This paper combines some of their results, unifies and simplifies their proofs, and adds discussion and examples.

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Maushagen, C., Rothe, J. Complexity of control by partitioning veto elections and of control by adding candidates to plurality elections. Ann Math Artif Intell 82, 219–244 (2018). https://doi.org/10.1007/s10472-017-9565-7

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Keywords

  • Computational social choice
  • Voting
  • Veto election
  • Control complexity

Mathematics Subject Classification (2010)

  • 91B14
  • 68Q17
  • 68Q15
  • 68T99