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Aggregation of Rankings in Figure Skating

Author

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  • Michel Truchon
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 firs 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

  • Michel Truchon, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0414, CIRPEE.
    • Handle: RePEc:lvl:lacicr:0414
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    References listed on IDEAS

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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. Truchon, Michel, 2008. "Borda and the maximum likelihood approach to vote aggregation," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 96-102, January.
    3. 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.
    4. 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.
    5. Michel Truchon, 2005. "Aggregation of Rankings: a Brief Review of Distance-Based Rules," Cahiers de recherche 0534, CIRPEE.
    6. Bargagliotti, Anna E., 2009. "Aggregation and decision making using ranked data," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 354-366, November.
    7. James Boudreau & Justin Ehrlich & Mian Farrukh Raza & Shane Sanders, 2018. "The likelihood of social choice violations in rank sum scoring: algorithms and evidence from NCAA cross country running," Public Choice, Springer, vol. 174(3), pages 219-238, March.
    8. Sasaki, Yasuo, 2023. "Strategic manipulation in group decisions with pairwise comparisons: A game theoretical perspective," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1133-1139.

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    More about this item

    Keywords

    Figure skating; ranking rules; vote aggregation; cycles; maximum likelihood; Kemeny; Copeland; Borda; manipulation;
    All these keywords.

    JEL classification:

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

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