Towards completing the puzzle: complexity of control by replacing, adding, and deleting candidates or voters

Erdélyi, Gábor; Neveling, Marc; Reger, Christian; Rothe, Jörg; Yang, Yongjie; Zorn, Roman

doi:10.1007/s10458-021-09523-9

Cited by 9 publications

(9 citation statements)

References 43 publications

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“…We connected the complexity of control by replacing voters for First-Last and 2-Approval elections to the complexity of the Exact Perfect [Bipartite] Matching, showing these problems in RP. For 2-Approval control by replacing voters, this shows the last remaining case in the comprehensive table from Erdélyi et al (2021) to be easy, since it is widely assumed P = RP. We expect this approach will be useful in exploring the complexity of other voting problems.…”

Section: Discussionmentioning

confidence: 99%

Insight into Voting Problem Complexity Using Randomized Classes

Fitzsimmons¹,

Hemaspaandra²

2022

Preprint

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The first step in classifying the complexity of an NP problem is typically showing the problem in P or NP-complete. This has been a successful first step for many problems, including voting problems. However, in this paper we show that this may not always be the best first step. We consider the problem of constructive control by replacing voters (CCRV) introduced by Loreggia et al. ( 2015) for the scoring rule First-Last, which is defined by 1, 0, . . . , 0, −1 . We show that this problem is equivalent to Exact Perfect Bipartite Matching (EPBM), and so CCRV for First-Last can be determined in random polynomial time. So on the one hand, if CCRV for First-Last is NP-complete then RP = NP, which is extremely unlikely. On the other hand, showing that CCRV for First-Last is in P would also show that Exact Perfect Bipartite Matching is in P, which would solve a well-studied 40-year-old open problem.Considering RP as an option for classifying problems can also help classify problems that until now had escaped classification. For example, the sole open problem in the comprehensive table from Erdélyi et al. ( 2021) is CCRV for 2-Approval. We show that this problem is in RP, and thus easy since it is widely assumed that P = RP.

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Section: Discussionmentioning

confidence: 99%

Insight into Voting Problem Complexity Using Randomized Classes

Fitzsimmons¹,

Hemaspaandra²

2022

Preprint

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“…For plurality with runoff, it was shown by Conitzer, Sandholm, and Lang [6] that unweighted coalitional manipulation is NP-hard. Finally, plurality with runoff and veto with runoff were also studied by Erdélyi et al [39] with respect to electoral control. This paper is organized as follows.…”

Section: Our Contribution and More Related Workmentioning

confidence: 99%

Complexity of shift bribery for iterative voting rules

Maushagen

Neveling

Rothe

et al. 2022

Ann Math Artif Intell

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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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“…The number of papers covering this theme is huge. We refer to (Baumeister and Rothe, 2016;Faliszewski and Rothe, 2016) and references therein for important progress by 2016, and refer to (Erdélyi et al, 2021;Yang, 2017Yang, , 2020b for some recent results.…”

Section: Related Workmentioning

confidence: 99%

“…The number of papers investigating the (parameterized) complexity of these problems for single-winner voting rules is enormous (see, e.g., [26,35,52]). We refer to the book chapters [6,27] for a consultation for results by 2016, and refer to [24,52,60,63] for some recent results.…”

Section: Related Work and Our Main Contributionsmentioning

confidence: 99%