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Nanson's and Baldwin's voting rules select a winner by successivelyeliminating candidates with low Borda scores. We show that these rules have anumber of desirable computational properties. In particular, with unweightedvotes, it is NP-hard to manipulate either rule with one manipulator, whilstwith weighted votes, it is NP-hard to manipulate either rule with a smallnumber of candidates and a coalition of manipulators. As only a couple of othervoting rules are known to be NP-hard to manipulate with a single manipulator,Nanson's and Baldwin's rules appear to be particularly resistant tomanipulation from a theoretical perspective. We also propose a number ofapproximation methods for manipulating these two rules. Experiments demonstratethat both rules are often difficult to manipulate in practice. These resultssuggest that elimination style voting rules deserve further study.

Manipulation of Nanson's and Baldwin's Rules