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Aggregation and decision making using ranked data

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  • Bargagliotti, Anna E.

Abstract

Nonparametric procedures are frequently used to rank order alternatives. Often, information from several data sets must be aggregated to derive an overall ranking. When using nonparametric procedures, Simpson-like paradoxes can occur in which the conclusion drawn from the aggregate ranked data set seems contradictory to the conclusions drawn from the individual data sets. Extending previous results found in the literature for the Kruskal-Wallis test, this paper presents a strict condition that ranked data must satisfy in order to avoid this type of inconsistency when using nonparametric pairwise procedures or Bhapkar's V procedure to extract an overall ranking. Aggregating ranked data poses further difficulties because there exist numerous ways to combine ranked data sets. This paper illustrates these difficulties and derives an upper bound for the number of possible ways that two ranked data sets can be combined.

Suggested Citation

  • Bargagliotti, Anna E., 2009. "Aggregation and decision making using ranked data," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 354-366, November.
    • Handle: RePEc:eee:matsoc:v:58:y:2009:i:3:p:354-366
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    References listed on IDEAS

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    1. Michel Truchon, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0414, CIRPEE.
    2. Raymond Stefani, 1997. "Survey of the major world sports rating systems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(6), pages 635-646.
    3. Deanna B. Haunsperger, 2003. "Aggregated statistical rankings are arbitrary," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(2), pages 261-272, March.
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    Cited by:

    1. Ozan Çakır & İbrahim Gürler & Bora Gündüzyeli, 2022. "Analysis of a Non-Discriminating Criterion in Simple Additive Weighting Deep Hierarchy," Mathematics, MDPI, vol. 10(17), pages 1-22, September.
    2. 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.
    3. Athanasios Spyridakos & Denis Yannacopoulos, 2015. "Incorporating collective functions to multicriteria disaggregation–aggregation approaches for small group decision making," Annals of Operations Research, Springer, vol. 227(1), pages 119-136, April.
    4. Berube, Sarah & Crisman, Karl-Dieter, 2011. "Decomposition behavior in aggregated data sets," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 12-19, January.

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