# On the Computational Complexity of Variants of Combinatorial Voter Control in Elections

• Leon Kellerhals
• Viatcheslav Korenwein
• Philipp Zschoche
• Robert Bredereck
• Jiehua Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10185)

## Abstract

Voter control problems model situations in which an external 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 candidate either win (constructive control) or lose (destructive control) the election. We study the constructive and destructive voter control problems when adding and deleting voters have a combinatorial flavor: If we add (resp. delete) a voter v, we also add (resp. delete) a bundle $$\kappa (v)$$ of voters that are associated with v. While the bundle $$\kappa (v)$$ 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 computationally easier than making her win. In particular, if the bundling relation is symmetric (i.e. $$\forall w:w \in \kappa (v) \Leftrightarrow v \in \kappa (w)$$), and if each voter has at most two voters associated with him, then destructive control is polynomial-time solvable while the constructive variant remains $$\mathsf {NP}$$-hard. Even if the bundles are disjoint (i.e. $$\forall w:w \in \kappa (v) \Leftrightarrow \kappa (v) = \kappa (w)$$), the constructive problem variants remain intractable. Finally, the minimization variant of constructive control by adding voters does not admit an efficient approximation algorithm, unless $$\mathsf {P}= \mathsf {NP}$$.

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© Springer International Publishing AG 2017

## Authors and Affiliations

• Leon Kellerhals
• 1
• Viatcheslav Korenwein
• 1
• Philipp Zschoche
• 1
• Robert Bredereck
• 1
• Jiehua Chen
• 1
Email author
1. 1.TU BerlinBerlinGermany