Control Complexity in Bucklin and Fallback Voting

Electoral control models ways of changing the outcome of an election via such actions as adding/deleting/partitioning either candidates or voters. These actions modify an election's participation structure and aim at either making a favorite candidate win ("constructive control") or prevent a despised candidate from winning ("destructive control"). To protect elections from such control attempts, computational complexity has been used to show that electoral control, though not impossible, is computationally prohibitive. We show that fallback voting, an election system proposed by Brams and Sanver to combine Bucklin with approval voting, is resistant to each of the common types of control except to destructive control by either adding or deleting voters. Thus fallback voting displays the broadest control resistance currently known to hold among natural election systems with a polynomial-time winner problem. We also study the control complexity of Bucklin voting itself and show that it behaves almost as good (possibly even as good) as fallback voting in terms of control resistance. As Bucklin voting is a special case of fallback voting, each resistance shown for Bucklin voting strengthens the corresponding resistance for fallback voting. Finally, we study the parameterized control complexity of Bucklin and fallback voting.