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Aggregation of Rankings in Figure Skating

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  • Truchon, Michel

Abstract

We scrutinize and compare, from the perspective of modern theory of social choice, two rules that have been used to rank competitors in Figure Skating for the past decades. The first rule has been in use at least from 1982 until 1998, when it was replaced by a new one. We also compare these two rules with the Borda and the Kemeny rules. The four rules are illustrated with examples and with the data of 30 Olympic competitions. The comparisons show that the choice of a rule can have a real impact on the rankings. In these data, we found as many as 19 cycles of the majority relation, involving as many as nine skaters. In this context, the Kemeny rule appears as a natural extension of the Condorcet rule. As a side result, we show that the Copeland rule can be used to partition the skaters in such a way that it suffice to find Kemeny rankings within subsets of the partition that are not singletons and then, to juxtapose these rankings to get a complete Kemeny ranking. We also propose the concept of the mean Kemeny ranking, which when it exists, may obviate the multiplicity of Kemeny rankings. Finally, the fours rules are examined in terms of their manipulability. It appears that the new rule used in Figure Skating may be more difficult to manipulate than the previous one but less so than the Kemeny rule.

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Bibliographic Info

Paper provided by Université Laval - Département d'économique in its series Cahiers de recherche with number 0402.

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Date of creation: 2004
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Handle: RePEc:lvl:laeccr:0402

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Keywords: Figure skating; ranking rules; vote aggregation; cycles; maximum likelihood; Kemeny; Copeland; Borda; manipulation;

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References

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  1. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
  2. Mohamed Drissi-Bakhkhat & Michel Truchon, 2004. "Maximum likelihood approach to vote aggregation with variable probabilities," Social Choice and Welfare, Springer, vol. 23(2), pages 161-185, October.
  3. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the probability that all decision rules select the same winner," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 183-207, March.
  4. Le Breton, M. & Truchon, M., 1993. "Acyclicity and the Dispersion of the Veto Power," Papers 9317, Laval - Recherche en Politique Economique.
  5. Saari, Donald G, 1990. " Susceptibility to Manipulation," Public Choice, Springer, vol. 64(1), pages 21-41, January.
  6. Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585, April.
  7. Jonathan Levin & Barry Nalebuff, 1995. "An Introduction to Vote-Counting Schemes," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 3-26, Winter.
  8. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
  9. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
  10. Barthelemy, J. P. & Guenoche, A. & Hudry, O., 1989. "Median linear orders: Heuristics and a branch and bound algorithm," European Journal of Operational Research, Elsevier, vol. 42(3), pages 313-325, October.
  11. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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Cited by:
  1. Michel Truchon, 2005. "Aggregation of Rankings: a Brief Review of Distance-Based Rules," Cahiers de recherche 0534, CIRPEE.
  2. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
  3. Michel Truchon, 2006. "Borda and the Maximum Likelihood Approach to Vote Aggregation," Cahiers de recherche 0623, CIRPEE.
  4. Bargagliotti, Anna E., 2009. "Aggregation and decision making using ranked data," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 354-366, November.
  5. Stephen Gordon & Michel Truchon, 2006. "Social Choice, Optimal Inference and Figure Skating," Cahiers de recherche 0624, CIRPEE.

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