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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.

Suggested Citation

  • Truchon, Michel, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0402, Université Laval - Département d'économique.
  • Handle: RePEc:lvl:laeccr:0402
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    File URL: http://www.ecn.ulaval.ca/w3/recherche/cahiers/2004/0402.pdf
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    References listed on IDEAS

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    1. 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.
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    5. Mohamed Drissi-Bakhkhat & Michel Truchon, 2004. "Maximum likelihood approach to vote aggregation with variable probabilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 161-185, October.
    6. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
    7. Saari, Donald G, 1990. "Susceptibility to Manipulation," Public Choice, Springer, vol. 64(1), pages 21-41, January.
    8. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
    9. 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.
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    Cited by:

    1. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
    2. Stephen Gordon & Michel Truchon, 2008. "Social choice, optimal inference and figure skating," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 265-284, February.
    3. Michel Truchon, 2005. "Aggregation of Rankings: a Brief Review of Distance-Based Rules," Cahiers de recherche 0534, CIRPEE.
    4. Truchon, Michel, 2008. "Borda and the maximum likelihood approach to vote aggregation," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 96-102, January.
    5. Bargagliotti, Anna E., 2009. "Aggregation and decision making using ranked data," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 354-366, November.
    6. Boudreau, James & Ehrlich, Justin & Sanders, Shane & Winn, Adam, 2014. "Social choice violations in rank sum scoring: A formalization of conditions and corrective probability computations," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 20-29.

    More about this item

    Keywords

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

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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