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Figure Skating and the Theory of Social Choice

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  • Truchon, M.

Abstract

The rule used by the United States Figure Skating Association and the International Skating Union, hereafter the ISU Rule, to aggregate individual rankings of the skaters by the judges into a final ranking, is an interesting example of a social welfare function. This rule is examined thoroughly in this paper from the perspective of the modern theory of social choice. The ISU Rule is based on four different criteria, the first being median ranks of the skaters. Although the median rank criterion is a majority principle, it is completely at odd with another majority principle introduced in this paper and called the Extended Condorcet Criterion. It may be translated as follows: If a competitor is ranked consistently ahead of another competitor by an absolute majority of judges, he should be ahead in the final ranking. Consistency here refers to the absence of a cycle in the majority relation involving these two skaters. There are actually many cycles in the data of four Olympic Games that were examined. The Kemeny rule may be used to break these cycles. This is not only consistent with the Extended Condorcet Criterion but the latter also proves useful in finding Kemeny orders over large sets of alternatives, by allowing decomposition of these orders. The ISU, the Kemeny, the Borda rankings and the ranking according to the raw marks are then compared on 24 olympic competitions. The four rankings disagree in many instances. Finally it is shown that the ISU Rule may be very sensitive to small errors on the part of the judges and that it does not escape the numerous theorems on manipulation. Some considerations are also offered as to whether the ISU Rule is more or less prone to manipulation than others.

Suggested Citation

  • Truchon, M., 1998. "Figure Skating and the Theory of Social Choice," Papers 9814, Laval - Recherche en Politique Economique.
    • Handle: RePEc:fth:lavape:9814
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    References listed on IDEAS

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    1. Le Breton, Michel & Truchon, Michel, 1997. "A Borda measure for social choice functions," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 249-272, October.
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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. 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.
    3. William Gehrlein, 2002. "Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences ," Theory and Decision, Springer, vol. 52(2), pages 171-199, March.
    4. Adrian Deemen, 2014. "On the empirical relevance of Condorcet’s paradox," Public Choice, Springer, vol. 158(3), pages 311-330, March.
    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. Harrison-Trainor, Matthew, 2022. "An analysis of random elections with large numbers of voters," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 68-84.
    7. Giuseppe Munda, 2012. "Intensity of preference and related uncertainty in non-compensatory aggregation rules," Theory and Decision, Springer, vol. 73(4), pages 649-669, October.
    8. 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.
    9. Azzini, Ivano & Munda, Giuseppe, 2020. "A new approach for identifying the Kemeny median ranking," European Journal of Operational Research, Elsevier, vol. 281(2), pages 388-401.
    10. Matthew Harrison-Trainor, 2020. "An Analysis of Random Elections with Large Numbers of Voters," Papers 2009.02979, arXiv.org.
    11. Giuseppe Munda & Michela Nardo, 2009. "Noncompensatory/nonlinear composite indicators for ranking countries: a defensible setting," Applied Economics, Taylor & Francis Journals, vol. 41(12), pages 1513-1523.
    12. Truchon, Michel, 1998. "An Extension of the Concordet Criterion and Kemeny Orders," Cahiers de recherche 9813, Université Laval - Département d'économique.

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    More about this item

    Keywords

    SOCIAL WELFARE;

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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