Abstract
In iterative voting systems, candidates are eliminated in consecutive rounds until either a fixed number of rounds is reached or the set of remaining candidates does not change anymore. We focus on iterative voting systems based on the positional scoring rules plurality, veto, and Borda and study their resistance against shift bribery attacks introduced by Elkind et al. [1] and Kaczmarczyk and Faliszewski [2]. In constructive shift bribery (Elkind et al. [1]), an attacker seeks to make a designated candidate win the election by bribing voters to shift this candidate in their preferences; in destructive shift bribery (Kaczmarczyk and Faliszewski [2]), the briber’s goal is to prevent this candidate’s victory. We show that many iterative voting systems are resistant to these types of attack, i.e., the corresponding decision problems are NP-hard. These iterative voting systems include iterated plurality as well as the voting rules due to Hare, Coombs, Baldwin, and Nanson; variants of Hare voting are also known as single transferable vote, instant-runoff voting, and alternative vote.
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16 October 2022
Springer Nature’s version of this paper was updated to reflect the Funding information: Open access funding provided by Open Access funding enabled and organized by Projekt DEAL
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We thank the anonymous AMAI, AAMAS’18, and ISAIM’18 reviewers for helpful comments.
Funding
Open access funding provided by Open Access funding enabled and organized by Projekt DEAL. This work was supported in part by Deutsche Forschungsgemeinschaft under grants RO 1202/21-1, RO 1202/15-1, RO 1202/14-2, and BA 6270/1-1.
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Author Jörg Rothe is or has been on the following editorial boards of scientific journals:
∙ Annals of Mathematics and Artificial Intelligence (AMAI), Associate Editor, since 01/2020,
∙ Journal of Artificial Intelligence Research (JAIR), Associate Editor, since 09/2017,
∙ Journal of Universal Computer Science (J.UCS), Editorial Board, since 01/2005,
∙ Mathematical Logic Quarterly (MLQ – Wiley), Editorial Board, 01/2008–12/2019, and
∙ MDPI Algorithms, Editorial Board, 04/2021–06/2022.
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Maushagen, C., Neveling, M., Rothe, J. et al. Complexity of shift bribery for iterative voting rules. Ann Math Artif Intell 90, 1017–1054 (2022). https://doi.org/10.1007/s10472-022-09802-5
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DOI: https://doi.org/10.1007/s10472-022-09802-5