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Combinatorial Models of Cross-Country Dual Meets: What is a Big Victory?

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  • Kurt S. Riedel

Abstract

Combinatorial/probabilistic models for cross-country dual-meets are proposed. The first model assumes that all runners are equally likely to finish in any possible order. The second model assumes that each team is selected from a large identically distributed population of potential runners and with each potential runner's ranking determined by the initial draw from the combined population.

Suggested Citation

  • Kurt S. Riedel, 2019. "Combinatorial Models of Cross-Country Dual Meets: What is a Big Victory?," Papers 1911.05044, arXiv.org.
    • Handle: RePEc:arx:papers:1911.05044
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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. 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.
    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. 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.
    5. 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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