Control Complexity in Fallback Voting

We study the control complexity of fallback voting. Like manipulation and bribery, electoral control describes ways of changing the outcome of an election; unlike manipulation or bribery attempts, control actions---such as adding/deleting/partitioning either candidates or voters---modify the participative structure of an election. Computational complexity can be used to protect elections from control attempts, i.e., proving an election system resistant to some type of control shows that the success of the corresponding control action, though not impossible, is computationally prohibitive. We show that fallback voting, an election system combining approval with majority voting (Brams & Sanver 2009), is resistant to each of the 14 common types of candidate control, and also to three types of voter control. The only election systems previously known to be fully resistant to candidate control are plurality (Bartholdi III et al. 1992, Hemaspaandra et al. 2007) and sincere-strategy preference-based approval voting (SP-AV) (Erdelyi et al. 2009). However, plurality has fewer resistances to voter control than fallback voting, and SP-AV (as modified by Erdelyi et al. (2009)) is arguably less natural a system than fallback voting.