Multivariate Complexity Analysis of Swap Bribery

Dorn, Britta; Schlotter, Ildikó

doi:10.1007/s00453-011-9568-4

Cited by 60 publications

(76 citation statements)

References 25 publications

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“…For a description of what we mean by "expressing the winner determination problem through integer linear inequalities," we point to the discussions by Dorn and Schlotter [8] or by Faliszewski et al [14]. For example, the result applies to all scoring rules.…”

Section: Generalizationsmentioning

confidence: 99%

“…and we ask whether a group of manipulators can cast votes to ensure their preferred candidate's victory), election control problems [2,17] (where we are given an election and ask if we can ensure a given candidate's victory by adding/deleting candidates/voters), or bribery [10,12,24] and campaign management problems [3,5,8,23] (where we want to ensure a given candidate's victory by changing some of the votes, but where each vote change comes at a price and we are bound by a budget). We focus on the case where we have a few candidates but (possibly) many voters.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Elections with Few Candidates: Prices, Weights, and Covering Problems

Bredereck

Faliszewski

Niedermeier

et al. 2015

Algorithmic Decision Theory

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Abstract. We show that a number of election-related problems with prices (such as, for example, bribery) are fixed-parameter tractable (in FPT) when parameterized by the number of candidates. For bribery, this resolves a nearly 10-year old family of open problems. Our results follow by a general technique that formulates voting problems as covering problems and extends the classic approach of using integer linear programming and the algorithm of Lenstra [19]. In this context, our central result is that WEIGHTED SET MULTICOVER parameterized by the universe size is fixed-parameter tractable. Our approach is also applicable to weighted electoral control for Approval voting. We improve previously known XP-memberships to FPT-memberships. Our preliminary experiments on real-world-based data show the practical usefulness of our approach for instances with few candidates.

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Section: Generalizationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Elections with Few Candidates: Prices, Weights, and Covering Problems

Bredereck

Faliszewski

Niedermeier

et al. 2015

Algorithmic Decision Theory

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“…Campaign management comprises all sorts of activities for influencing the outcome of an election, including well-known scenarios such as bribery (Faliszewski, Hemaspaandra, & Hemaspaandra, 2009;Dorn & Schlotter, 2012;Schlotter, Elkind, & Faliszewski, 2011;Elkind, Faliszewski, & Slinko, 2012) and control (Bartholdi III, Tovey, & Trick, 1992;Elkind, Faliszewski, & Slinko, 2011;Erdélyi, Piras, & Rothe, 2011). While these works relate to campaigning in case of classical voting scenarios where one typically wants to make a specific candidate win or to prevent him from winning, Christian, Fellows, Rosamond, and Slinko (2007) introduced the scenario of lobbying in multiple referenda.…”

Section: Introductionmentioning

confidence: 99%

A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

Bredereck

Hartung

Kratsch

et al. 2014

jair

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Assume that each of n voters may or may not approve each of m issues. If an agent (the lobby) may influence up to k voters, then the central question of the NP-hard Lobbying problem is whether the lobby can choose the voters to be influenced so that as a result each issue gets a majority of approvals. This problem can be modeled as a simple matrix modification problem: Can one replace k rows of a binary n×m-matrix by k all-1 rows such that each column in the resulting matrix has a majority of 1s? Significantly extending on previous work that showed parameterized intractability (W[2]-completeness) with respect to the number k of modified rows, we study how natural parameters such as n, m, k, or the "maximum number of 1s missing for any column to have a majority of 1s" (referred to as "gap value g") govern the computational complexity of Lobbying. Among other results, we prove that Lobbying is fixed-parameter tractable for parameter m and provide a greedy logarithmic-factor approximation algorithm which solves Lobbying even optimally if m ≤ 4. We also show empirically that this greedy algorithm performs well on general instances. As a further key result, we prove that Lobbying is LOGSNP-complete for constant values g ≥ 1, thus providing a first natural complete problem from voting for this complexity class of limited nondeterminism.

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“…One of the most important parameterized complexity classes for this purpose is W [2] (see Section 2 for more details). We remark in passing that a parameterized complexity analysis has been employed for several other voting problems, (e.g., see Brandt, Brill, & Seedig, 2011;Betzler, Guo, & Niedermeier, 2010;Betzler, Hemmann, & Niedermeier, 2009;Christian, Fellows, Rosamond, & Slinko, 2007;Dorn & Schlotter, 2010;Elkind, Faliszewski, & Slinko, 2010b;Rothe, 2009a andalso Betzler, Bredereck, Chen, &Niedermeier, 2012 for a survey).…”

Section: Our Approach and Results For General Electionsmentioning

confidence: 99%

On the Computation of Fully Proportional Representation

Betzler

Slinko

Uhlmann

2013

jair

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We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the "sum of misrepresentations" is minimized. The winner determination problem for both systems is known to be NP-hard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximal misrepresentation introducing effectively two new rules. In the general case these "minimax" versions of classical rules appeared to be still NP-hard.We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners.For single-peaked electorates our results are overwhelmingly positive: we provide polynomial-time algorithms for most of the considered problems. The only rule that remains NP-hard for single-peaked electorates is the classical Monroe rule.

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Multivariate Complexity Analysis of Swap Bribery

Cited by 60 publications

References 25 publications

Elections with Few Candidates: Prices, Weights, and Covering Problems

Elections with Few Candidates: Prices, Weights, and Covering Problems

A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

On the Computation of Fully Proportional Representation

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