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The aggregation paradox for statistical rankings and nonparametric tests

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  • Haikady N Nagaraja
  • Shane Sanders

Abstract

The relationship between social choice aggregation rules and non-parametric statistical tests has been established for several cases. An outstanding, general question at this intersection is whether there exists a non-parametric test that is consistent upon aggregation of data sets (not subject to Yule-Simpson Aggregation Paradox reversals for any ordinal data). Inconsistency has been shown for several non-parametric tests, where the property bears fundamentally upon robustness (ambiguity) of non-parametric test (social choice) results. Using the binomial(n, p = 0.5) random variable CDF, we prove that aggregation of r(≥2) constituent data sets—each rendering a qualitatively-equivalent sign test for matched pairs result—reinforces and strengthens constituent results (sign test consistency). Further, we prove that magnitude of sign test consistency strengthens in significance-level of constituent results (strong-form consistency). We then find preliminary evidence that sign test consistency is preserved for a generalized form of aggregation. Application data illustrate (in)consistency in non-parametric settings, and links with information aggregation mechanisms (as well as paradoxes thereof) are discussed.

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  • 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.
    • Handle: RePEc:plo:pone00:0228627
    DOI: 10.1371/journal.pone.0228627
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    1. Sven Stringer & Naomi R Wray & René S Kahn & Eske M Derks, 2011. "Underestimated Effect Sizes in GWAS: Fundamental Limitations of Single SNP Analysis for Dichotomous Phenotypes," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-7, November.
    2. Koessler, Frédéric & Noussair, Charles & Ziegelmeyer, Anthony, 2012. "Information aggregation and belief elicitation in experimental parimutuel betting markets," Journal of Economic Behavior & Organization, Elsevier, vol. 83(2), pages 195-208.
    3. Hausman, Jerry A & Newey, Whitney K, 1995. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Econometrica, Econometric Society, vol. 63(6), pages 1445-1476, November.
    4. Akritas, Michael G. & Antoniou, Efi S. & Kuha, Jouni, 2006. "Nonparametric Analysis of Factorial Designs With Random Missingness: Bivariate Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1513-1526, December.
    5. Miller, Joshua Benjamin & Sanjurjo, Adam, 2018. "Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers," OSF Preprints sv9x2, Center for Open Science.
    6. Alessandro Selvitella, 2017. "The ubiquity of the Simpson’s Paradox," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-16, December.
    7. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
    8. Datta, Somnath & Satten, Glen A., 2005. "Rank-Sum Tests for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 908-915, September.
    9. Bargagliotti, Anna E., 2009. "Aggregation and decision making using ranked data," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 354-366, November.
    10. Hanson, Robin & Oprea, Ryan & Porter, David, 2006. "Information aggregation and manipulation in an experimental market," Journal of Economic Behavior & Organization, Elsevier, vol. 60(4), pages 449-459, August.
    11. Jan De Neve & Olivier Thas, 2015. "A Regression Framework for Rank Tests Based on the Probabilistic Index Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1276-1283, September.
    12. Bennouri, Moez & Gimpel, Henner & Robert, Jacques, 2011. "Measuring the impact of information aggregation mechanisms: An experimental investigation," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 302-318, May.
    13. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    14. Jiangtao Gou & Fengqing (Zoe) Zhang, 2017. "Experience Simpson's Paradox in the Classroom," The American Statistician, Taylor & Francis Journals, vol. 71(1), pages 61-66, January.
    15. Vartia, Yrjo O, 1983. "Efficient Methods of Measuring Welfare Change and Compensated Income in Terms of Ordinary Demand Functions," Econometrica, Econometric Society, vol. 51(1), pages 79-98, January.
    16. Briesch, Richard A. & Chintagunta, Pradeep K. & Matzkin, Rosa L., 2010. "Nonparametric Discrete Choice Models With Unobserved Heterogeneity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 291-307.
    17. Li Hao & Daniel Houser, 2015. "Adaptive Procedures for the Wilcoxon–Mann–Whitney Test: Seven Decades of Advances," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(9), pages 1939-1957, May.
    18. 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.
    19. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-270, March.
    20. Axelrod, Boris S. & Kulick, Ben J. & Plott, Charles R. & Roust, Kevin A., 2009. "The design of improved parimutuel-type information aggregation mechanisms: Inaccuracies and the long-shot bias as disequilibrium phenomena," Journal of Economic Behavior & Organization, Elsevier, vol. 69(2), pages 170-181, February.
    21. Gur Yaari & Shmuel Eisenmann, 2011. "The Hot (Invisible?) Hand: Can Time Sequence Patterns of Success/Failure in Sports Be Modeled as Repeated Random Independent Trials?," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-10, October.
    22. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    23. William Gehrlein & Florenz Plassmann, 2014. "A comparison of theoretical and empirical evaluations of the Borda Compromise," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 747-772, October.
    24. Kaufmann, Christine & Weber, Martin, 2013. "Sometimes less is more – The influence of information aggregation on investment decisions," Journal of Economic Behavior & Organization, Elsevier, vol. 95(C), pages 20-33.
    25. Debopam Bhattacharya, 2015. "Nonparametric Welfare Analysis for Discrete Choice," Econometrica, Econometric Society, vol. 83, pages 617-649, March.
    26. 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.
    27. Joshua B. Miller & Adam Sanjurjo, 2018. "Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers," Econometrica, Econometric Society, vol. 86(6), pages 2019-2047, November.
    28. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    29. Pavlides, Marios G. & Perlman, Michael D., 2009. "How Likely Is Simpson’s Paradox?," The American Statistician, American Statistical Association, vol. 63(3), pages 226-233.
    30. 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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