Parameterized Control Complexity in Bucklin Voting and in Fallback Voting1

We study the parameterized control complexity of Bucklin voting and of fallback voting, a voting system that combines Bucklin voting with approval voting. Electoral control is one of many different ways for an external agent to tamper with the outcome of an election. We show that even though the representation of the votes and the winner determination is different, the parameterized complexity of some standard control attacks is the same. In particular, we show that adding and deleting candidates in both voting systems are W[2]-hard for both the constructive and destructive case, parameterized by the amount of action taken by the external agent. Furthermore, we show that adding and deleting voters in both Bucklin voting and fallback voting are W[2]-hard for the constructive case, parameterized again by the amount of action taken by the external agent, and are in FPT for the destructive case.