TY - GEN

T1 - On the approximability of dodgson and young elections

AU - Caragiannis, Ioannis

AU - Covey, Jason A.

AU - Feldman, Michal

AU - Homan, Christopher M.

AU - Kaklamanis, Christos

AU - Karanikolas, Nikos

AU - Procaccia, Ariel D.

AU - Rosenschein, Jeffrey S.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70349125827&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973068.115

DO - 10.1137/1.9781611973068.115

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AN - SCOPUS:70349125827

SN - 9780898716801

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1058

EP - 1067

BT - Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms

PB - Association for Computing Machinery (ACM)

T2 - 20th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 4 January 2009 through 6 January 2009

ER -