• Speaker: Nina Narodytska
  • Title: Complexity of and Algorithms for Borda Manipulation
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Tue, 10th Jan 2012
  • Abstract:

    We prove the 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.

    We also consider Nanson’s and Baldwin’s voting rules that select a winner by successively eliminating candidates with low Borda scores. We theoretically and experimentally demonstrate that these rules are significantly more difficult to manipulate compared to Borda rule. 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.

  • [Permanent link]