Abstract
We propose O⁎((m⋅2m)t+1)-time and O⁎((t+m−1t)⋅(t+1)m)-time algorithms for the weighted and the unweighted Borda manipulation problems, respectively, where t is the number of manipulators and m is the number of candidates. In particular, for t=2, our algorithm for the unweighted case runs in O⁎(3m) time, affirmatively resolving one open problem posed by Betzler et al. [2]. As a byproduct of our results, we show that the unweighted Borda manipulation problem admits an algorithm with running time O⁎(29m2logm), based on an integer linear programming technique. Finally, we prove that the unweighted Borda manipulation problem is polynomial-time solvable in single-peaked elections, in contrast to the NP-hardness in the general case.
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