  Electoral control models ways of changing the outcome of an election via such
actions as adding/deleting/partitioning either candidates or voters. To protect
elections from such control attempts, computational complexity has been
investigated and the corresponding NP-hardness results are termed "resistance."
It has been a long-running project of research in this area to classify the
major voting systems in terms of their resistance properties. We show that
fallback voting, an election system proposed by Brams and Sanver (2009) 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 and show that it
performs at least almost as well 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. Such worst-case complexity analysis is at best an
indication of security against control attempts, rather than a proof. In
practice, the difficulty of control will depend on the structure of typical
instances. We investigate the parameterized control complexity of Bucklin and
fallback voting, according to several parameters that are often likely to be
small for typical instances. Our results, though still in the worst-case
complexity model, can be interpreted as significant strengthenings of the
resistance demonstrations based on NP-hardness.
