On the approximability of dodgson and young elections

Ioannis Caragiannis, Jason A. Covey, Michal Feldman, Christopher M. Homan, Christos Kaklamanis, Nikos Karanikolas, Ariel D. Procaccia, Jeffrey S. Rosenschein

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

Abstract

The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorithms for approximating the Dodgson score: an LP-based randomized rounding algorithm and a deterministic greedy algorithm, both of which yield an script O(log m) approximation ratio, where m is the number of alternatives; we observe that this result is asymptotically optimal, and further prove that our greedy algorithm is optimal up to a factor of 2, unless problems in script N℘ have quasi-polynomial time algorithms. Although the greedy algorithm is computationally superior, we argue that the randomized rounding algorithm has an advantage from a social choice point of view. Further, we demonstrate that computing any reasonable approximation of the ranking produced by Dodgson's rule is script N℘-hard. This result provides a complexity-theoretic explanation of sharp discrepancies that have been observed in the Social Choice Theory literature when comparing Dodgson elections with simpler voting rules. Finally, we show that the problem of calculating the Young score is script N℘-hard to approximate by any factor. This leads to an inapproximability result for the Young ranking.

Original languageEnglish
Title of host publicationProceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms
PublisherAssociation for Computing Machinery (ACM)
Pages1058-1067
Number of pages10
ISBN (Print)9780898716801
DOIs
StatePublished - 2009
Externally publishedYes
Event20th Annual ACM-SIAM Symposium on Discrete Algorithms - New York, NY, United States
Duration: 4 Jan 20096 Jan 2009

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference20th Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CityNew York, NY
Period4/01/096/01/09

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