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How Hard Is Bribery in Elections?
| Citations: | 55 - 21 self |
BibTeX
@MISC{Faliszewski_howhard,
author = {Piotr Faliszewski and Edith Hemaspaandra and Lane A. Hemaspaandra},
title = {How Hard Is Bribery in Elections?},
year = {}
}
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Abstract
We study the complexity of influencing elections through bribery: How computationally complex is it for an external actor to determine whether by paying certain voters to change their preferences a specified candidate can be made the election’s winner? We study this problem for election systems as varied as scoring protocols and Dodgson voting, and in a variety of settings regarding homogeneous-vs.-nonhomogeneous electorate bribability, bounded-size-vs.-arbitrary-sized candidate sets, weighted-vs.-unweighted voters, and succinct-vs.-nonsuccinct input specification. We obtain both polynomial-time bribery algorithms and proofs of the intractability of bribery, and indeed our results show that the complexity of bribery is extremely sensitive to the setting. For example, we find settings in which bribery is NP-complete but manipulation (by voters) is in P, and we find settings in which bribing weighted voters is NP-complete but bribing voters with individual bribe thresholds is in P. For the broad class of elections (including plurality, Borda, k-approval, and veto) known as scoring protocols, we prove a dichotomy result for bribery of weighted voters: We find a simple-to-evaluate condition that classifies every case as either NP-complete or in P. 1.
Keyphrases
scoring protocol individual bribe threshold nonsuccinct input specification specified candidate broad class arbitrary-sized candidate set weighted voter dichotomy result unweighted voter external actor election winner dodgson voting election system simple-to-evaluate condition certain voter nonhomogeneous electorate bribability polynomial-time bribery algorithm
