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Using equations from power indices to analyze figure skating teams

Author

Listed:
  • Diana Cheng

    (Towson University)

  • Peter Coughlin

    (University of Maryland)

Abstract

Power indices were originally developed to measure voting power. However, Saari and Sieberg (Games Econ Behav 36:241–263, 2001) and Saari (Chaotic elections, American Mathematical Society, Providence, 2001a) have suggested that the equations from power indices could potentially be used in some sports contexts as a way of evaluating athletes. This article explores this idea in the context of figure skating. The International Skating Union developed team events in figure skating for the 2014 Winter Olympic Games in Sochi, Russia and for other major competitions. In this article, we show how the Shapley–Shubik and Banzhaf indices can be used to analyze contributions of athletes to their countries’ teams in figure skating team events. We illustrate this approach by analyzing the results from the 2014 Winter Olympic Games figure skating team event. We also discuss some ways in which the numbers assigned by the equations from power indices can be used in the figure skating context.

Suggested Citation

  • Diana Cheng & Peter Coughlin, 2017. "Using equations from power indices to analyze figure skating teams," Public Choice, Springer, vol. 170(3), pages 231-251, March.
    • Handle: RePEc:kap:pubcho:v:170:y:2017:i:3:d:10.1007_s11127-016-0392-x
    DOI: 10.1007/s11127-016-0392-x
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    References listed on IDEAS

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    1. Boudreau, James W. & Sanders, Shane, 2015. "Choosing “Flawed” aggregation rules: The benefit of social choice violations in a league that values competitive balance," Economics Letters, Elsevier, vol. 137(C), pages 106-108.
    2. van Deemen, Adrian & Rusinowska, Agnieszka, 2003. "Paradoxes of Voting Power in Dutch Politics," Public Choice, Springer, vol. 115(1-2), pages 109-137, April.
    3. Nicholas Miller, 2012. "Why the Electoral College is good for political science (and public choice)," Public Choice, Springer, vol. 150(1), pages 1-25, January.
    4. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    5. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, June.
    6. D. Kilgour & Terrence Levesque, 1984. "The Canadian constitutional amending formula: Bargaining in the past and the future," Public Choice, Springer, vol. 44(3), pages 457-480, January.
    7. Bassett, Gilbert W, Jr & Persky, Joseph, 1999. "Robust Voting," Public Choice, Springer, vol. 99(3-4), pages 299-310, June.
    8. Ansgar Belke & Barbara Schnurbein, 2012. "European monetary policy and the ECB rotation model," Public Choice, Springer, vol. 151(1), pages 289-323, April.
    9. Thomas Hammond, 2007. "Rank injustice?: How the scoring method for cross-country running competitions violates major social choice principles," Public Choice, Springer, vol. 133(3), pages 359-375, December.
    10. 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.
    11. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489, March.
    12. 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.
    13. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    14. Franklin G. Mixon Jr. & Ernest W. King, 2012. "Social Choice Theory in 10,000 Meters: Examining Independence and Transitivity in the Ncaa Cross-Country Championships," The American Economist, Sage Publications, vol. 57(1), pages 32-41, May.
    15. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, June.
    16. repec:bla:econom:v:52:y:1985:i:206:p:167-83 is not listed on IDEAS
    17. Saari, Donald G. & Sieberg, Katri K., 2001. "Some Surprising Properties of Power Indices," Games and Economic Behavior, Elsevier, vol. 36(2), pages 241-263, August.
    18. Leech, Dennis, 2002. "Designing the Voting System for the Council of the European Union," Public Choice, Springer, vol. 113(3-4), pages 437-464, December.
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    More about this item

    Keywords

    Voting power; Shapley–Shubik index; Banzhaf index; Figure skating; Olympics;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • Z20 - Other Special Topics - - Sports Economics - - - General

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