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Aggregated statistical rankings are arbitrary

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  • Deanna B. Haunsperger

Abstract

In many areas of mathematics, statistics, and the social sciences, the intriguing, and somewhat unsettling, paradox occurs where the “parts” may give rise to a common decision, but the aggregate of those parts, the “whole”, gives rise to a different decision. The Kruskal-Wallis nonparametric statistical test on n samples which can be used to rank-order a list of alternatives is subject to such a Simpson-like paradox of aggregation. That is, two or more data sets each may individually support a certain ordering of the samples under Kruskal-Wallis, yet their union, or aggregate, yields a different outcome. An analysis of this phenomenon yields a computable criterion which characterizes which matrices of ranked data, when aggregated, can give rise to such a paradox. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:20:y:2003:i:2:p:261-272
    DOI: 10.1007/s003550200179
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    Cited by:

    1. Nurmi, Hannu, 2005. "Aggregation problems in policy evaluation: an overview," European Journal of Political Economy, Elsevier, vol. 21(2), pages 287-300, June.
    2. Bargagliotti, Anna E., 2009. "Aggregation and decision making using ranked data," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 354-366, November.
    3. 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.
    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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