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Algorithms for Destructive Shift Bribery

Andrzej Kaczmarczyk (AGH University, Krakow, Poland)


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 (ranking the candidates from best to worst, each), a despised candidate d (typically, one of the current winners), a budget B, and prices for shifting d down in 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 all scoring protocols (encoded in unary) and the Maximin rule, but is NP-hard for the Copeland rule. This contrasts with 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.


Andrzej Kaczmarczyk
TEL 512

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