Multivariate Complexity Analysis of Swap Bribery

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 NPhardness for a slightly more general scenario. We obtain fixed-parameter tractability as well as W[1]-hardness results for certain natural parameters.

• Type: Journal
• Year: 2010
• Where: IWPEC
• Authors: Britta Dorn, Ildikó Schlotter
• Keywords: Applied Computing, Computational Complexity, IWPEC 2010, Multivariate Complexity Analysis, Swap Bribery