  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. Via such actions one can try to either
make a favorite candidate win ("constructive control") or prevent a despised
candidate from winning ("destructive control"). 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, is resistant to each of the common types of
candidate control and to each common type of constructive control. Among
natural election systems with a polynomial-time winner problem, only plurality
and sincere-strategy preference-based approval voting (SP-AV) were previously
known to be fully resistant to candidate control, and only Copeland voting and
SP-AV were previously known to be fully resistant to constructive control.
However, plurality has fewer resistances to voter control, Copeland voting has
fewer resistances to destructive control, and SP-AV (which like fallback voting
has 19 out of 22 proven control resistances) is arguably less natural a system
than fallback voting.
