On the complexity of bribery with distance restrictions

Abstract We study the complexity of the constructive/destructive bribery problem with distance restrictions. In the constructive/destructive bribery problem, we are given an election and a distinguished candidate p, and are asked whether we can make p a winner/loser by bribing a limited number of voters to recast their votes. In the constructive/destructive bribery problem with distance restrictions, we require that the votes recast by the bribed voters are close to their original votes. In particular, we measure the closeness of two votes by the minimum number of swaps of candidates needed to transform one vote into the other. We consider both the case where swaps only take place between consecutive candidates, and the case where swaps can take place between any arbitrary candidates. We achieve a wide range of complexity results for the voting correspondences Borda, Condorcet, Copeland α for every rational number 0 ≤ α ≤ 1 , and Maximin.

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