Elections with Few Voters: Candidate Control Can Be Easy

Abstract

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.

Towards completing the puzzle: complexity of control by replacing, adding, and deleting candidates or voters

“…As mentioned in the introduction, since the seminal work of Bartholdi, Tovey, and Trick [7] control by adding and deleting candidates or voters has been extensively studied in the literature (see, e.g., [11,17,34,44,49,60,62]). However, the complexity of control by replacing candidates or voters has been introduced and studied just recently by Loreggia et al [40][41][42][43].…”

Winner Determination and Strategic Control in Conditional Approval Voting

“…Furthermore, a different instrument for the controller is to add more choices for the issues under consideration or delete existing ones, towards enforcing her will. We refer to [Chen et al, 2017] for related examples. It is reasonable to assume that the controller does not have unlimited power, and therefore, she is capable of adding/deleting only a certain number of voters/alternatives.…”

The complexity of priced control in elections

“…This counting variant of control can be used to predict election winners and, thus, has similar applications as the research presented in this paper; it aims to guide the election campaigning process. Recently, Bulteau et al [11] and Chen et al [12] considered combinatorial control, where adding each candidate or voter may result in adding some other ones as well. This variant of control also is useful from the point of view of campaign management.…”