TY - JOUR

T1 - Resolute control

T2 - Forbidding candidates from winning an election is hard

AU - Gupta, Sushmita

AU - Roy, Sanjukta

AU - Saurabh, Saket

AU - Zehavi, Meirav

N1 - Funding Information:
Supported by SERB-Starting Research Grant (SRG/2019/001870).Supported by the WWTF research grant (VRG18-012).Supported by European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant no. 819416), and Swarnajayanti Fellowship grant DST/SJF/MSA-01/2017-18. [Formula presented] [Formula presented]Supported by ISF grant (no. 1176/18) and BSF grant (no. 2018302).
Publisher Copyright:
© 2022 The Author(s)

PY - 2022/5/14

Y1 - 2022/5/14

N2 - We study a set of voting problems where given an election E=(C,ΠV) (where C is the set of candidates and ΠV is a set of votes), and a non-empty subset of candidates J, the question under consideration is: Can we modify the election in a way so that none of the candidates in J wins the election? The modification operations allowed are that of either adding or deleting some candidates. Yang and Wang (2017) [44] introduced these problems as the RESOLUTE CONTROL problem, a generalization of the destructive control problem where J is a singleton. They studied parameterized complexity of RESOLUTE CONTROL for voting rules Borda (both addition and deletion), Maximin (addition), and Copeland (both addition and deletion). They primarily consider |J| as parameter. In this paper we study RESOLUTE CONTROL parameterized by the other natural parameters viz., the number of candidates added or deleted. We show that the RESOLUTE CONTROL for Borda (both addition and deletion), Maximin (addition) and Copeland (deletion) are W[2]-hard. We complement this by showing that when the number of voters is odd, Copeland (deletion) is FPT parameterized by the sum of the number of deleted candidates and the size of the feedback arc set of the majority graph of the election.

AB - We study a set of voting problems where given an election E=(C,ΠV) (where C is the set of candidates and ΠV is a set of votes), and a non-empty subset of candidates J, the question under consideration is: Can we modify the election in a way so that none of the candidates in J wins the election? The modification operations allowed are that of either adding or deleting some candidates. Yang and Wang (2017) [44] introduced these problems as the RESOLUTE CONTROL problem, a generalization of the destructive control problem where J is a singleton. They studied parameterized complexity of RESOLUTE CONTROL for voting rules Borda (both addition and deletion), Maximin (addition), and Copeland (both addition and deletion). They primarily consider |J| as parameter. In this paper we study RESOLUTE CONTROL parameterized by the other natural parameters viz., the number of candidates added or deleted. We show that the RESOLUTE CONTROL for Borda (both addition and deletion), Maximin (addition) and Copeland (deletion) are W[2]-hard. We complement this by showing that when the number of voters is odd, Copeland (deletion) is FPT parameterized by the sum of the number of deleted candidates and the size of the feedback arc set of the majority graph of the election.

KW - Parameterized complexity

KW - Resolute control

KW - Voting

KW - W-hardness

UR - http://www.scopus.com/inward/record.url?scp=85126083320&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2022.02.031

DO - 10.1016/j.tcs.2022.02.031

M3 - Article

AN - SCOPUS:85126083320

SN - 0304-3975

VL - 915

SP - 74

EP - 89

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -