A comparison of Dodgson's method and the Borda count

Ratliff, Thomas

doi:10.1007/s001990100218

Cited by 31 publications

(18 citation statements)

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“…It will be shown that the Copeland rule ranks alternatives according to their distances to being Condorcet winners. The use of distance information in preference aggregation problems in a finite framework goes back to Dodgson [4] and distance-based aggregation rules are discussed in recent papers by Saari and Merlin [16], Ratliff [13,14] and Klamler [9,10]. 2 The next section sets out the formal framework.…”

Section: Introductionmentioning

confidence: 99%

The Copeland rule and Condorcet?s principle

Klamler

2005

Economic Theory

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Section: Introductionmentioning

confidence: 99%

The Copeland rule and Condorcet?s principle

Klamler

2005

Economic Theory

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“…Some of the results mentioned above [28,29,18,19,20] establish that there are sharp discrepancies between the Dodgson ranking and the rankings produced by other rank aggregation rules. Some of these rules (e.g., Borda and Copeland) are polynomial-time computable, so the corresponding results can be viewed as negative results regarding the approximability of the Dodgson ranking by polynomial-time algorithms.…”

Section: Introductionmentioning

confidence: 93%

“…There exists β > 0 such that it is N P-hard to approximate the Dodgson score of a given alternative in an election with m alternatives to within a factor of β ln m. Furthermore, for any > 0, there is no polynomial-time A related question is the approximability of the Dodgson ranking, that is, the ranking of alternatives given by ordering them by nondecreasing Dodgson score. To the best of our knowledge, no rank aggregation function, which maps preferences profiles to rankings of the alternatives, is known to provably produce rankings that are close to the Dodgson rank- ing [28,29,18,19,20] (see the survey of related work in Section 1).…”

Section: Lower Boundsmentioning

confidence: 99%

“…Such comparisons have always revealed sharp discrepancies. For example, the Dodgson winner can appear in any position in the Kemeny ranking [28] and in the ranking of any positional scoring rule [29] (e.g., Borda or Plurality), Dodgson rankings can be exactly the opposite of Borda [20] and Copeland rankings [18], while the winner of Kemeny of Slater elections can appear in any position of the Dodgson ranking [19].…”

Section: Introductionmentioning

confidence: 99%

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On the Approximability of Dodgson and Young Elections

Caragiannis¹,

Covey²,

Feldman³

et al. 2009

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

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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 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 N P 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 N P-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 N P-hard to approximate by any factor. This leads to an inapproximability result for the Young ranking.

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“…Other authors also proposed alternative distance-based aggregation rules e.g., Eckert and Klamler [19], Klamler [44,43], Meskanen and Nurmi [50], Ratliff [52,53], and Saari and Merlin [54], even though Kemeny's rule [39] could be considered as a landmark in aggregation procedures based on distances. Following Kemeny's rule, Cook and Seiford [14] established an equivalence between the Borda-Kendall method [40] and their approach.…”

Section: Introductionmentioning

confidence: 99%

A new consensus ranking approach for correlated ordinal information based on Mahalanobis distance

González-Arteaga

Alcantud

Calle

2016

Information Sciences

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We investigate from a global point of view the existence of cohesiveness among experts' opinions. We address this general issue from three basic essentials: the management of experts' opinions when they are expressed by ordinal information; the measurement of the degree of dissensus among such opinions; and the achievement of a group solution that conveys the minimum dissensus to the experts' group. Accordingly, we propose and characterize a new procedure to codify ordinal information. We also define a new measurement of the degree of dissensus among individual preferences based on the Mahalanobis distance. It is especially designed for the case of possibly correlated alternatives. Finally, we investigate a procedure to obtain a social consensus solution that also includes the possibility of alternatives that are correlated. In addition, we examine the main traits of the dissensus measurement as well as the social solution proposed. The operational character and intuitive interpretation of our approaches are illustrated by an explanatory example.

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A comparison of Dodgson's method and the Borda count

Cited by 31 publications

References 4 publications

The Copeland rule and Condorcet?s principle

The Copeland rule and Condorcet?s principle

On the Approximability of Dodgson and Young Elections

A new consensus ranking approach for correlated ordinal information based on Mahalanobis distance

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