Complexity of and Algorithms for Borda Manipulation


  • Jessica Davies University of Toronto
  • George Katsirelos LRI, Universite Paris Sud 11
  • Nina Narodytska NICTA and University of New South Wales
  • Toby Walsh NICTA and University of New South Wales


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 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.




How to Cite

Davies, J., Katsirelos, G., Narodytska, N., & Walsh, T. (2011). Complexity of and Algorithms for Borda Manipulation. Proceedings of the AAAI Conference on Artificial Intelligence, 25(1), 657-662. Retrieved from



AAAI Technical Track: Multiagent Systems