, Volume 64, Issue 1, pp 126–151 | Cite as

Multivariate Complexity Analysis of Swap Bribery

  • Britta Dorn
  • Ildikó SchlotterEmail author


We consider the computational complexity of a problem modeling bribery in the context of voting systems. In the scenario of Swap Bribery, each voter assigns a certain price for swapping the positions of two consecutive candidates in his preference ranking. The question is whether it is possible, without exceeding a given budget, to bribe the voters in a way that the preferred candidate wins in the election.

We initiate a parameterized and multivariate complexity analysis of Swap Bribery, focusing on the case of k-approval. We investigate how different cost functions affect the computational complexity of the problem. We identify a special case of k-approval for which the problem can be solved in polynomial time, whereas we prove NP-hardness for a slightly more general scenario. We obtain fixed-parameter tractability as well as W[1]-hardness results for certain natural parameters.


Computational social choice Parameterized complexity Swap Bribery 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Fakultät für Mathematik und WirtschaftswissenschaftenUniversität UlmUlmGermany
  2. 2.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

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