  Successive elimination of candidates is often a route to making manipulation
intractable to compute. We prove that eliminating candidates does not
necessarily increase the computational complexity of manipulation. However, for
many voting rules used in practice, the computational complexity increases. For
example, it is already known that it is NP-hard to compute how a single voter
can manipulate the result of single transferable voting (the elimination
version of plurality voting). We show here that it is NP-hard to compute how a
single voter can manipulate the result of the elimination version of veto
voting, of the closely related Coombs' rule, and of the elimination versions of
a general class of scoring rules.
