Large-Scale Election Campaigns: Combinatorial Shift Bribery

Bredereck, Robert; Faliszewski, Piotr; Niedermeier, Rolf; Talmon, Nimrod

doi:10.1613/jair.4927

Cited by 26 publications

(20 citation statements)

References 42 publications

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“…In this we continue our previous work, conducted by a slightly different set of authors, on combinatorial voter control (Bulteau, Chen, Faliszewski, Niedermeier, & Talmon, 2015) and combinatorial shift bribery (Bredereck, Faliszewski, Niedermeier, & Talmon, 2016b). We mention that a somewhat similar model of combinatorial control was also studied by Erdélyi, Hemaspaandra, and Hemaspaandra (2015).…”

Section: Introductionsupporting

confidence: 62%

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Elections with Few Voters: Candidate Control Can Be Easy

Faliszewski¹,

Niedermeier²,

Talmon³

2017

jair

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We study the computational complexity of candidate control in elections with few voters, that is, we consider the parameterized complexity of candidate control in elections with respect to the number of voters as a parameter. We consider both the standard scenario of adding and deleting candidates, where one asks whether a given candidate can become a winner (or, in the destructive case, can be precluded from winning) by adding or deleting few candidates, as well as a combinatorial scenario where adding/deleting a candidate automatically means adding or deleting a whole group of candidates. Considering several fundamental voting rules, our results show that the parameterized complexity of candidate control, with the number of voters as the parameter, is much more varied than in the setting with many voters.

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Section: Introductionsupporting

confidence: 62%

“…Kellerhals, Korenwein, Zschoche, Bredereck, and Chen (2017) extended our work and investigated other types of combinatorial voter control problems. A different notion of combinatorial control was studied by Erdélyi et al (2015), and some of us also considered combinatorial shift bribery (Bredereck et al, 2016b).…”

Section: Related Workmentioning

confidence: 99%

Elections with Few Voters: Candidate Control Can Be Easy

Faliszewski¹,

Niedermeier²,

Talmon³

2017

jair

Self Cite

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“…We have also shown more efficient versions of our algorithms for the case of the Borda rule with unit prices. Our PTAS improves upon the 2-approximation algorithm of Elkind et al [EFS09,EF10], but their algorithm is quite robust and was used, e.g., for combinatorial shift bribery [BFNT16] and bribery in approval elections [FST17]. It may be possible to apply our technique in these settings as well.…”

Section: Discussionmentioning

confidence: 99%

Approximation and Hardness of Shift-Bribery

Faliszewski

Manurangsi

Sornat

2019

AAAI

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In the SHIFT-BRIBERY problem we are given an election, a preferred candidate, and the costs of shifting this preferred candidate up the voters' preference orders. The goal is to find such a set of shifts that ensures that the preferred candidate wins the election. We give the first polynomial-time approximation scheme for the SHIFT-BRIBERY problem for the case of positional scoring rules, and for the Copeland rule we show strong inapproximability results. * An extended abstract of this work appears in AAAI'19.

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“…Chen et al [4] considered parametrized complexity of Constructive Shift Bribery, and have shown a varied set of results (in general, parametrization by the number of positions by which the preferred candidate is shifted tends to lead to FPT algorithms, parametrization by the number of affected voters tends to lead to hardness results, and parametrization by the available budget gives results between these two extremes). Recently, Bredereck et al [6] studied the complexity of Combinatorial Shift Bribery, where a single shift action can affect several voters at a time. Their paper is quite related to ours, because it was the first one in which shifting a candidate backward was possible (albeit as a negative side effect, since the authors studied the constructive setting).…”

Section: Related Workmentioning

confidence: 99%

Algorithms for destructive shift bribery

Kaczmarczyk

Faliszewski

2019

Auton Agent Multi-Agent Syst

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We study the complexity of Destructive Shift Bribery. In this problem, we are given an election with a set of candidates and a set of voters (each ranking the candidates from the best to the worst), a despised candidate d, a budget B, and prices for shifting d back in the voters' rankings. The goal is to ensure that d is not a winner of the election. We show that this problem is polynomial-time solvable for scoring protocols (encoded in unary), the Bucklin and Simplified Bucklin rules, and the Maximin rule, but is NPhard for the Copeland rule. This stands in contrast to the results for the constructive setting (known from the literature), for which the problem is polynomial-time solvable for k-Approval family of rules, but is NP-hard for the Borda, Copeland, and Maximin rules. We complement the analysis of the Copeland rule showing W-hardness for the parameterization by the budget value, and by the number of affected voters. We prove that the problem is W-hard when parameterized by the number of voters even for unit prices. From the positive perspective we provide an efficient algorithm for solving the problem parameterized by the combined parameter the number of candidates and the maximum bribery price (alternatively the number of different bribery prices).

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Large-Scale Election Campaigns: Combinatorial Shift Bribery

Cited by 26 publications

References 42 publications

Elections with Few Voters: Candidate Control Can Be Easy

Elections with Few Voters: Candidate Control Can Be Easy

Approximation and Hardness of Shift-Bribery

Algorithms for destructive shift bribery

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