We consider the computational complexity of a problem modeling
in the context of voting systems. In the scenario of
, 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
, focusing on the case of
-approval. We investigate how different cost functions affect the computational complexity of the problem. We identify a special case of
-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-hardness results for certain natural parameters.