STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs
SIAM Journal on Computing
Voting for movies: the anatomy of a recommender system
Proceedings of the third annual conference on Autonomous Agents
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Approximating Bounded Degree Instances of NP-Hard Problems
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Ordering by weighted number of wins gives a good ranking for weighted tournaments
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Aggregating inconsistent information: Ranking and clustering
Journal of the ACM (JACM)
The learnability of voting rules
Artificial Intelligence
On distance rationalizability of some voting rules
Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge
Computing slater rankings using similarities among candidates
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Improved bounds for computing Kemeny rankings
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Socially desirable approximations for Dodgson's voting rule
Proceedings of the 11th ACM conference on Electronic commerce
On the role of distances in defining voting rules
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Multimode control attacks on elections
Journal of Artificial Intelligence Research
Fully proportional representation as resource allocation: approximability results
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Guest column: the elusive inapproximability of the TSP
ACM SIGACT News
Hi-index | 0.00 |
The voting rules proposed by Dodgson and Young are both designed to find an 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: a combinatorial, greedy algorithm and an LP-based algorithm, both of which yield an approximation ratio of H"m"-"1, where m is the number of alternatives and H"m"-"1 is the (m-1)st harmonic number. We also prove that our algorithms are optimal within a factor of 2, unless problems in NP have quasi-polynomial-time algorithms. Despite the intuitive appeal of the greedy algorithm, we argue that the LP-based 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 NP-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 NP-hard to approximate by any factor. This leads to an inapproximability result for the Young ranking.