Abstract
“Control” studies attempts to set the outcome of elections through the addition, deletion, or partition of voters or candidates. The set of benchmark control types was largely set in the 1992 paper by Bartholdi, Tovey, and Trick that introduced control, and there now is a large literature studying how many of the benchmark types various election systems are vulnerable to, i.e., have polynomial-time attack algorithms for.
However, although the longstanding benchmark models of addition and deletion model relatively well the real-world settings that inspire them, the longstanding benchmark models of partition model settings that are arguably quite distant from those they seek to capture.
In this paper, we introduce—and for some important cases analyze the complexity of—new partition models that seek to better capture many real-world partition settings. In particular, in many partition settings one wants the two parts of the partition to be of (almost) equal size, or is partitioning into more than two parts, or has groups of actors who must be placed in the same part of the partition. Our hope is that having these new partition types will allow studies of control attacks to include such models that more realistically capture many settings.
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Notes
- 1.
This paper contains some NP-completeness results, the first of which is Theorem 2. NP-completeness is a worst-case theory, and so for our paper’s NP-hard cases, seeking results for other notions of hardness would be interesting. See [25, 26] for successes of and [19] for limitations of heuristic approaches to election (and other) problems. However, the majority of the present paper’s results are about showing that, even for partition-control variants that might seem likely to increase control complexity, polynomial-time control algorithms do exist.
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Acknowledgments
Supported by COST Action IC1205 and grants DFG-ER-738/{1-1,2-1} and NSF-CCF-{0915792,1101452,1101479}. We thank the anonymous referees.
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Erdélyi, G., Hemaspaandra, E., Hemaspaandra, L.A. (2015). More Natural Models of Electoral Control by Partition. 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_24
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