  In 1992, Bartholdi, Tovey, and Trick opened the study of control attacks on
elections---attempts to improve the election outcome by such actions as
adding/deleting candidates or voters. That work has led to many results on how
algorithms can be used to find attacks on elections and how
complexity-theoretic hardness results can be used as shields against attacks.
However, all the work in this line has assumed that the attacker employs just a
single type of attack. In this paper, we model and study the case in which the
attacker launches a multipronged (i.e., multimode) attack. We do so to more
realistically capture the richness of real-life settings. For example, an
attacker might simultaneously try to suppress some voters, attract new voters
into the election, and introduce a spoiler candidate. Our model provides a
unified framework for such varied attacks, and by constructing polynomial-time
multiprong attack algorithms we prove that for various election systems even
such concerted, flexible attacks can be perfectly planned in deterministic
polynomial time.
