TY - GEN

T1 - On the computational complexity of variants of combinatorial voter control in elections

AU - Kellerhals, Leon

AU - Korenwein, Viatcheslav

AU - Zschoche, Philipp

AU - Bredereck, Robert

AU - Chen, Jiehua

N1 - Funding Information:
R. Bredereck—From September 2016 to September 2017 on postdoctoral leave at the University of Oxford (GB), supported by the DFG fellowship BR 5207/2.
Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Voter control problems model situations in which an exter-nal agent tries to affect the result of an election by adding or deleting the fewest number of voters. The goal of the agent is to make a specific can-didate either win (constructive control) or lose (destructive control) the election. We study the constructive and destructive voter control prob-lems when adding and deleting voters have a combinatorial flavor: If we add (resp. delete) a voter v, we also add (resp. delete) a bundle κ(v) of voters that are associated with v. While the bundle κ(v) may have more than one voter, a voter may also be associated with more than one voter. We analyze the computational complexity of the four voter control problems for the Plurality rule. We obtain that, in general, making a candidate lose is computation-ally easier than making her win. In particular, if the bundling relation is symmetric (i.e. ∀w: w ∈ κ(v) ⇔ v ∈ κ(w)), and if each voter has at most two voters associated with him, then destructive control is polynomial-time solvable while the constructive variant remains NP-hard. Even if the bundles are disjoint (i.e. ∀w: w ∈ κ(v) ⇔ κ(v) = κ(w)), the con-structive problem variants remain intractable. Finally, the minimization variant of constructive control by adding voters does not admit an eﬃ-cient approximation algorithm, unless P = NP.

AB - Voter control problems model situations in which an exter-nal agent tries to affect the result of an election by adding or deleting the fewest number of voters. The goal of the agent is to make a specific can-didate either win (constructive control) or lose (destructive control) the election. We study the constructive and destructive voter control prob-lems when adding and deleting voters have a combinatorial flavor: If we add (resp. delete) a voter v, we also add (resp. delete) a bundle κ(v) of voters that are associated with v. While the bundle κ(v) may have more than one voter, a voter may also be associated with more than one voter. We analyze the computational complexity of the four voter control problems for the Plurality rule. We obtain that, in general, making a candidate lose is computation-ally easier than making her win. In particular, if the bundling relation is symmetric (i.e. ∀w: w ∈ κ(v) ⇔ v ∈ κ(w)), and if each voter has at most two voters associated with him, then destructive control is polynomial-time solvable while the constructive variant remains NP-hard. Even if the bundles are disjoint (i.e. ∀w: w ∈ κ(v) ⇔ κ(v) = κ(w)), the con-structive problem variants remain intractable. Finally, the minimization variant of constructive control by adding voters does not admit an eﬃ-cient approximation algorithm, unless P = NP.

UR - http://www.scopus.com/inward/record.url?scp=85018451140&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-55911-7_25

DO - 10.1007/978-3-319-55911-7_25

M3 - Conference contribution

AN - SCOPUS:85018451140

SN - 9783319559100

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 348

EP - 361

BT - Theory and Applications of Models of Computation - 14th Annual Conference, TAMC 2017, Proceedings

A2 - Jager, Gerhard

A2 - Steila, Silvia

A2 - Gopal, T.V.

PB - Springer Verlag

T2 - 14th Annual Conference on Theory and Applications of Models of Computation, TAMC 2017

Y2 - 20 April 2017 through 22 April 2017

ER -