On the approximability of Dodgson and Young elections

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

doi:10.1016/j.artint.2012.04.004

Cited by 17 publications

(17 citation statements)

References 29 publications

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“…There are now very good approximation algorithms for Kemeny's rule [1,16,28] and for Dodgson's rule [10,11,20,26,38]. In both cases the results are, in essence, optimal.…”

Section: Related Workmentioning

confidence: 89%

“…In both cases the results are, in essence, optimal. For Kemeny's rule there is a polynomial-time approximation scheme [28] (although the running time of this algorithm is not very practical) and for Dodgson's rule the achieved approximation ratio is optimal under standard complexity-theoretic assumptions [10] (unfortunately, the approximation ratio is not constant but depends logarithmically on the number of candidates). On the other hand, for Young's rule it is known that no good approximation algorithms exist [10].…”

Section: Related Workmentioning

confidence: 98%

“…The competitions include European skating championships, Olympic Games, World Junior, and World Championships, all from 1998. 10 (Note that while in figure skating judges provide numerical scores, this data set is preprocessed to contain preference orders. )…”

Section: Figurementioning

confidence: 99%

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Achieving fully proportional representation: Approximability results

Skowron

Faliszewski

Slinko

2015

Artificial Intelligence

136

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We study the complexity of (approximate) winner determination under the Monroe and Chamberlin-Courant multiwinner voting rules, which determine the set of representatives by optimizing the total satisfaction or dissatisfaction of the voters with their representatives. The total (dis)satisfaction is calculated either as the sum of individual (dis)satisfactions in the utilitarian case or as the (dis)satisfaction of the worst off voter in the egalitarian case. We provide good approximation algorithms for the satisfaction-based utilitarian versions of the Monroe and Chamberlin-Courant rules, and inapproximability results for the dissatisfaction-based utilitarian versions of these rules and also for all egalitarian cases. Our algorithms are applicable and particularly appealing when voters submit truncated ballots. We provide experimental evaluation of the algorithms both on real-life preference-aggregation data and on synthetic preference data. These experiments show that our simple and fast algorithms can, in many cases, find near-perfect solutions.

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“…There are now very good approximation algorithms for Kemeny's rule [1,16,28] and for Dodgson's rule [10,11,20,26,38]. In both cases the results are, in essence, optimal.…”

Section: Related Workmentioning

confidence: 89%

Section: Related Workmentioning

confidence: 98%

See 1 more Smart Citation

Achieving fully proportional representation: Approximability results

Skowron

Faliszewski

Slinko

2015

Artificial Intelligence

136

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“…Finally, we mention that in the years since the work showing Lewis Carroll's election system to have a winner problem that is complete for parallel access to NP, a number of other systems, most notably those of Kemeny and Young, have also been shown to be complete for parallel access to NP. 33,43 Naturally, researchers have sought to bypass these hardness results as well (for examples, see 6,9,12,36 ).…”

Section: Review Articlesmentioning

confidence: 97%

“…35 Another way of arguably bypassing the hardness results for the Lewis Carroll winner problem is through approximation algorithms. For example, Caragiannis et al 9 have recently developed two approximation algorithms for computing candidates' scores in Carroll's system. And a third way to sidestep the hardness results is to change the framework, namely, to assume that the number of candidates or the number of voters is bounded by a fi xed constant, and to seek polynomial-time algorithms in that setting.…”

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confidence: 99%

Using complexity to protect elections

2010

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Democratix: A Declarative Approach to Winner Determination

Charwat

Pfandler

2015

Algorithmic Decision Theory

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Computing the winners of an election is an important subtask in voting and preference aggregation. The declarative nature of answer-set programming (ASP) and the performance of state-of-the-art solvers render ASP very well-suited to tackle this problem. In this work we present a novel, reduction-based approach for a variety of voting rules, ranging from tractable cases to problems harder than NP. In addition, we discuss how encodings of voting rules can be optimized and combined in our approach. The encoded voting rules are put together in the extensible tool DEMOCRATIX, which handles the computation of the winners and is also available as a web application.To learn more about the capabilities and limits of the approach, the encodings are evaluated thoroughly on real-world data as well as on random instances.

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On the approximability of Dodgson and Young elections

Cited by 17 publications

References 29 publications

Achieving fully proportional representation: Approximability results

Achieving fully proportional representation: Approximability results

Using complexity to protect elections

Democratix: A Declarative Approach to Winner Determination

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