  Nanson's and Baldwin's voting rules select a winner by successively
eliminating candidates with low Borda scores. We show that these rules have a
number of desirable computational properties. In particular, with unweighted
votes, it is NP-hard to manipulate either rule with one manipulator, whilst
with weighted votes, it is NP-hard to manipulate either rule with a small
number of candidates and a coalition of manipulators. As only a couple of other
voting rules are known to be NP-hard to manipulate with a single manipulator,
Nanson's and Baldwin's rules appear to be particularly resistant to
manipulation from a theoretical perspective. We also propose a number of
approximation methods for manipulating these two rules. Experiments demonstrate
that both rules are often difficult to manipulate in practice. These results
suggest that elimination style voting rules deserve further study.
