Abstract
We consider the computational complexity of a problem modeling bribery in the context of voting systems. In the scenario of Swap Bribery, each voter assigns a certain price for swapping the positions of two consecutive candidates in his preference ranking. The question is whether it is possible, without exceeding a given budget, to bribe the voters in a way that the preferred candidate wins in the election.
We initiate a parameterized and multivariate complexity analysis of Swap Bribery, focusing on the case of k-approval. We investigate how different cost functions affect the computational complexity of the problem. We identify a special case of k-approval for which the problem can be solved in polynomial time, whereas we prove NP-hardness for a slightly more general scenario. We obtain fixed-parameter tractability as well as W[1]-hardness results for certain natural parameters.
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I. Schlotter is supported by the Hungarian National Research Fund (OTKA 67651), and by the European Union and the European Social Fund (grant TÁMOP 4.2.1./B-09/1/KMR-2010-0003).
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Dorn, B., Schlotter, I. Multivariate Complexity Analysis of Swap Bribery. Algorithmica 64, 126–151 (2012). https://doi.org/10.1007/s00453-011-9568-4
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DOI: https://doi.org/10.1007/s00453-011-9568-4