TY - JOUR AU - Davies, Jessica AU - Katsirelos, George AU - Narodytska, Nina AU - Walsh, Toby PY - 2011/08/04 Y2 - 2024/03/28 TI - Complexity of and Algorithms for Borda Manipulation JF - Proceedings of the AAAI Conference on Artificial Intelligence JA - AAAI VL - 25 IS - 1 SE - AAAI Technical Track: Multiagent Systems DO - 10.1609/aaai.v25i1.7873 UR - https://ojs.aaai.org/index.php/AAAI/article/view/7873 SP - 657-662 AB - <p> 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. </p> ER -