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The likelihood of social choice violations in rank sum scoring: algorithms and evidence from NCAA cross country running

Author

Listed:
  • James Boudreau

    (Kennesaw State University)

  • Justin Ehrlich

    (Western Illinois University)

  • Mian Farrukh Raza

    (Kansas State University)

  • Shane Sanders

    (Syracuse University)

Abstract

Recent contributions have used combinatorial algorithms to determine the likelihood of particular social choice violations in rank sum scoring. Given the broad importance of rank sum scoring (e.g., in non-parametric statistical testing, sporting competition, and mathematical competition), it is important to establish the level of ambiguity generated by this aggregation rule. Combinatorial likelihoods are naïve, however, in that they assume each possible outcome sequence for an event to be equally likely. We develop a computational algorithm to extend upon previous combinatorial results as to the likelihood of a violation of transitivity or independence in rank sum scoring. We use a similar computational scoring approach to analyze the empirically-observed likelihood of each such violation across fourteen NCAA Cross Country Championships. Within the data, rank sum scoring fails to specify a robust winning team (i.e., one that also rank sum wins against each possible subset of opponents) in 4 of 14 cases. Overall, we find that empirical likelihoods of social choice violations are consistently (significantly) overestimated by combinatorial expectations. In the NCAA data, we find correlated ability (quality) levels within team (group) and discuss this as a cause of lower empirical likelihoods. Combinatorial analysis proves reliable in predicting the order of empirical likelihoods across violation type and event setting.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:pubcho:v:174:y:2018:i:3:d:10.1007_s11127-017-0494-0
    DOI: 10.1007/s11127-017-0494-0
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    References listed on IDEAS

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    1. Truchon, Michel, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0402, Université Laval - Département d'économique.
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    8. 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.
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    Cited by:

    1. Haikady N Nagaraja & Shane Sanders, 2020. "The aggregation paradox for statistical rankings and nonparametric tests," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-21, March.
    2. Shane Sanders & Joel Potter & Justin Ehrlich & Justin Perline & Christopher Boudreaux, 2021. "Informed voters and electoral outcomes: a natural experiment stemming from a fundamental information-technological shift," Public Choice, Springer, vol. 189(1), pages 257-277, October.
    3. Ram Sewak Dubey & Giorgio Laguzzi, 2022. "How rare are the properties of binary relations?," Papers 2202.05229, arXiv.org.
    4. Justin Ehrlich & Simon Medcalfe & Shane Sanders, 2021. "Composite Index Ranking of Economic Well-Being in U.S. Metropolitan Areas: How Prevalent are Rank Anomalies?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 157(2), pages 543-562, September.
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    6. 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.
    7. Kurt S. Riedel, 2019. "Combinatorial Models of Cross-Country Dual Meets: What is a Big Victory?," Papers 1911.05044, arXiv.org.

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