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

Leon Kellerhals, Viatcheslav Korenwein, Philipp Zschoche, Robert Bredereck, Jiehua Chen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publicationTheory and Applications of Models of Computation - 14th Annual Conference, TAMC 2017, Proceedings
EditorsGerhard Jager, Silvia Steila, T.V. Gopal
PublisherSpringer Verlag
Pages348-361
Number of pages14
ISBN (Print)9783319559100
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes
Event14th Annual Conference on Theory and Applications of Models of Computation, TAMC 2017 - Bern, Switzerland
Duration: 20 Apr 201722 Apr 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10185 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th Annual Conference on Theory and Applications of Models of Computation, TAMC 2017
Country/TerritorySwitzerland
CityBern
Period20/04/1722/04/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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