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Social Choice Theory in 10,000 Meters: Examining Independence and Transitivity in the Ncaa Cross-Country Championships

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  • Franklin G. Mixon Jr.
  • Ernest W. King

Abstract

A recent study by Hammond (2007) delves into scoring methods in athletic events as a way of illuminating social choice problems. Hammond's study indicates, using data from a girls' high school cross-country meet in Michigan, that the current scoring method for high school cross-country is plagued by two problems related to inconsistency and ambiguity in the results – problems that can be characterized as violations of the principles of independence from irrelevant teams (IIT) and transitivity. Our note supports and extends Hammond's study by examining the results from both the 2008 and 2009 NCAA Division I men's cross-country championships, wherein the types of scoring problems found by Hammond are present. Unlike high school-level cross-country, however, we show that salaries, bonuses, and budgets at the collegiate level can be substantial, so that any inconsistencies and ambiguities in the scoring mechanism can be quite costly for individuals and institutions.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:amerec:v:57:y:2012:i:1:p:32-41
    DOI: 10.1177/056943451205700103
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    References listed on IDEAS

    as
    1. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, October.
    2. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, October.
    3. 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.
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    Cited by:

    1. Kurt S. Riedel, 2019. "Combinatorial Models of Cross-Country Dual Meets: What is a Big Victory?," Papers 1911.05044, arXiv.org.
    2. 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.
    3. 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.
    4. 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.
    5. Shane Sanders & Justin Ehrlich & James Boudreau, 2024. "Rule selection invariance as a robustness check in collective choice and nonparametric statistical settings," Public Choice, Springer, vol. 199(1), pages 7-26, April.
    6. 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.

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