Prices matter for the parameterized complexity of shift bribery

In the Shift Bribery problem, we are given an election, a preferred candidate p, and a budget. The goal is to ensure p's victory by shifting p higher in some voters' preference orders. However, each such shift request comes at a price and we must not exceed the given budget. We study the p...

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Bibliographic Details
Published in:Information and computation Vol. 251; pp. 140 - 164
Main Authors: Bredereck, Robert, Chen, Jiehua, Faliszewski, Piotr, Nichterlein, André, Niedermeier, Rolf
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2016
Subjects:
Computational social choice
Fixed-parameter tractability (FPT)
FPT approximation scheme
Multivariate complexity analysis
Voting and rank aggregation
W-hardness
W-hardness
Computational social choice
Fixed-parameter tractability (FPT)
FPT approximation scheme
Voting and rank aggregation
Multivariate complexity analysis
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:In the Shift Bribery problem, we are given an election, a preferred candidate p, and a budget. The goal is to ensure p's victory by shifting p higher in some voters' preference orders. However, each such shift request comes at a price and we must not exceed the given budget. We study the parameterized computational complexity of Shift Bribery for a number of parameters and several classes of price functions: For the number of affected voters, Shift Bribery is W[2]-hard for Borda, Maximin, and Copeland. For the number of positions by which p is shifted in total, the problem is fixed-parameter tractable for Borda and Maximin, and is W[1]-hard for Copeland. For the budget, the results depend on the price function class. Finally, Shift Bribery tends to be tractable when parameterized by the number of voters, but the results for the number of candidates are more enigmatic.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2016.08.003