The aggregation paradox for statistical rankings and nonparametric tests

PLoS One. 2020 Mar 12;15(3):e0228627. doi: 10.1371/journal.pone.0228627. eCollection 2020.

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.

MeSH terms

  • Choice Behavior
  • Interpersonal Relations*
  • Statistics, Nonparametric*

Grants and funding

The author(s) received no specific funding for this work.