Algorithms for destructive shift bribery

Abstract

We study the complexity of Destructive Shift Bribery. In this problem, we are given an election with a set of candidates and a set of voters (each ranking the candidates from the best to the worst), a despised candidate d, a budget B, and prices for shifting d back in the voters' rankings. The goal is to ensure that d is not a winner of the election. We show that this problem is polynomial-time solvable for scoring protocols (encoded in unary), the Bucklin and Simplified Bucklin rules, and the Maximin rule, but is NPhard for the Copeland rule. This stands in contrast to the results for the constructive setting (known from the literature), for which the problem is polynomial-time solvable for k-Approval family of rules, but is NP-hard for the Borda, Copeland, and Maximin rules. We complement the analysis of the Copeland rule showing W-hardness for the parameterization by the budget value, and by the number of affected voters. We prove that the problem is W-hard when parameterized by the number of voters even for unit prices. From the positive perspective we provide an efficient algorithm for solving the problem parameterized by the combined parameter the number of candidates and the maximum bribery price (alternatively the number of different bribery prices).

Generalized Distance Bribery

“…The following formula is a straightforward generalization of the formula presented by Kaczmarczyk and Faliszewski (2016) for destructive shift bribery. By f (i, r) with i ∈ {1, 2, .…”

“…We continue, by considering the destructive variant of distance bribery for Borda elections. It is known that destructive shift bribery and destructive unweighted swap bribery are in P for Borda (see, e. g., Kaczmarczyk and Faliszewski (2016) and Shiryaev et al (2013)). In contrast we will show NP-completeness for DESTRUCTIVE DISTANCE BRIBERY for a class of pure scoring rules, including Borda, when using the weighted swap distance.…”

Opinion Diffusion and Campaigning on Society Graphs

“…For the case of swap bribery, Dorn and Schlotter [17] provided a careful analysis for the case of approval voting, whereas Knop et al [36] gave a general FPT algorithm parameterized by the number of candidates. Both problems were also studied in the destructive setting, where the goal is to prevent a given candidate from being a winner [31,48]. Interestingly, in this case the problem is often efficiently solvable.…”

Robustness Among Multiwinner Voting Rules

“…This problem is strongly connected to some other problems studied in the literature. Specifically, in the Destructive Swap Bribery problem [12,24,15] (DSB for short) we ask if it is possible to preclude a particular candidate from winning by making a given number of swaps. DSB was already used to study robustness of single-winner election rules by Shiryaev et al [24].…”