Abstract
In apportionment elections, a fixed number of seats in a parliament are distributed to parties according to their vote counts. Common procedures are divisor sequence methods like D’Hondt or Sainte-Laguë. In many countries, an electoral threshold is used to prevent very small parties from entering the parliament. Parties with fewer than a given number of votes are simply removed. We (experimentally) show that by exploiting this threshold, the effectiveness of strategic campaigns (where an external agent seeks to change the outcome by bribing voters) can be increased significantly, and prove that it is computationally easy to determine the required actions. To resolve this, we propose an alternative second-chance mode where voters of parties below the threshold receive a second chance to vote for another party. We establish complexity results showing that this makes elections more resistant to strategic campaigns.
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Notes
- 1.
Note that in strategic campaigns, as we define them, the total number of voters never changes but only which party they vote for. Thus the threshold is also constant.
- 2.
Note that in the top-choice mode it would be sufficient to know the top choice of each voter. However, we need the full preference later in the second-chance mode. So for convenience, we assume complete rankings for both modes.
- 3.
Here, we removed votes from the dataset which are labeled ‘none of the above’.
- 4.
- 5.
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Acknowledgements
This work was supported in part by DFG grant RO-1202/21-1. We thank Niclas Boehmer, Robert Bredereck, and Martin Bullinger for their helpful comments during a seminar at Schloss Dagstuhl.
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Laußmann, C., Rothe, J., Seeger, T. (2024). Apportionment with Thresholds: Strategic Campaigns are Easy in the Top-Choice but Hard in the Second-Chance Mode. In: Fernau, H., Gaspers, S., Klasing, R. (eds) SOFSEM 2024: Theory and Practice of Computer Science. SOFSEM 2024. Lecture Notes in Computer Science, vol 14519. Springer, Cham. https://doi.org/10.1007/978-3-031-52113-3_25
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