Complexity of and Algorithms for Borda Manipulation
  We prove that it is NP-hard for a coalition of two manipulators to compute
how to manipulate the Borda voting rule. This resolves one of the last open
problems in the computational complexity of manipulating common voting rules.
Because of this NP-hardness, we treat computing a manipulation as an
approximation problem where we try to minimize the number of manipulators.
Based on ideas from bin packing and multiprocessor scheduling, we propose two
new approximation methods to compute manipulations of the Borda rule.
Experiments show that these methods significantly outperform the previous best
known %existing approximation method. We are able to find optimal manipulations
in almost all the randomly generated elections tested. Our results suggest
that, whilst computing a manipulation of the Borda rule by a coalition is
NP-hard, computational complexity may provide only a weak barrier against
manipulation in practice.
