Approximating bribery in scoring rules

Orgad Keller, Avinatan Hassidim, Noam Hazon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations


The classic bribery problem is to find a minimal subset of voters who need to change their vote to make some preferred candidate win. We find an approximate solution for this problem for a broad family of scoring rules (which includes Borda and t-approval), in the following sense: if there is a strategy which requires bribing k voters, we efficiently find a strategy which requires bribing at most k + O(k) voters. Our algorithm is based on a randomized reduction from bribery to coalitional manipulation (UCM). To solve the UCM problem, we apply the Birkhoff-von Neumann (BvN) decomposition to a fractional manipulation matrix. This allows us to limit the size of the possible ballot search space reducing it from exponential to polynomial, while still obtaining good approximation guarantees. Finding the optimal solution in the truncated search space yields a new algorithm for UCM, which is of independent interest.

Original languageEnglish
Title of host publication32nd AAAI Conference on Artificial Intelligence, AAAI 2018
PublisherAAAI press
Number of pages9
ISBN (Electronic)9781577358008
StatePublished - 2018
Event32nd AAAI Conference on Artificial Intelligence, AAAI 2018 - New Orleans, United States
Duration: 2 Feb 20187 Feb 2018

Publication series

Name32nd AAAI Conference on Artificial Intelligence, AAAI 2018


Conference32nd AAAI Conference on Artificial Intelligence, AAAI 2018
Country/TerritoryUnited States
CityNew Orleans

Bibliographical note

Funding Information:
This work was supported by the Israel Science Foundation, under Grant No. 1488/14 and Grant No. 1394/16.

Publisher Copyright:
Copyright © 2018, Association for the Advancement of Artificial Intelligence ( All rights reserved.


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