Manipulation with Bounded Single-Peaked Width: A Parameterized Study

We study the manipulation problem in elections with bounded singlepeaked width from the parameterized complexity point of view. In particular, we focus on the Borda, Copeland and Maximin voting correspondences. For Borda, we prove that the unweighted manipulation problem with two manipulators is fixed-parameter tractable with respect to single-peaked width. For Maximin and Copeland for every 0 ≤ α ≤ 1, we prove that the unweighted manipulation problem is fixed-parameter tractable with respect to the combined parameter (k, t), where k denotes the single-peaked width and t denotes the number of manipulators. In addition, we study the weighted manipulation problem for Maximin and Copeland for every 0 ≤ α ≤ 1 in single-peaked elections and achieve several polynomial-time solvability results.