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Rule selection invariance as a robustness check in collective choice and nonparametric statistical settings.
- Source :
- Public Choice; Apr2024, Vol. 199 Issue 1/2, p7-26, 20p
- Publication Year :
- 2024
-
Abstract
- This study establishes conditional equivalence between Borda rule and rank sum collective choice. We apply the equivalence condition toward a comparison of the Wilcoxon–Mann–Whitney (WMW) rank sum test and sign test in non-parametric statistics, where the sign test is shown to be procedurally-equivalent to pairwise Borda rule aggregation. We further establish a social choice theoretic robustness check on the WMW test by determining whether a significant WMW rank sum winner could be a raw Borda loser (i.e., could have a p-value greater than 0.5 in a corresponding one-sided sign test). We then test whether a significant sign test winner could be a raw WMW winner. The WMW test is robust against significant victory by a raw Borda loser for almost all small sample cases (specifically, for n < 27 ) at any standard significance level (i.e., for α ≤ 0.10) . The sign test is robust against significant victory by a raw rank sum loser only for n < 14 at any standard significance level. The results provide caution against using the α = 0.10 significance level in some small sample cases of the WMW test. The robustness checks developed herein can be used generally or specifically to check whether a given set of non-parametric data passes the robustness check or whether significance for one test guarantees raw victory in the alternative test (for a given sample size n) in general. These robustness checks present a methodology to test for a weak form of qualitative equivalence across non-parametric tests. We develop a web application (http://avisss.com/visualization/RankSumHistograms.html) for such robustness checks. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00485829
- Volume :
- 199
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Public Choice
- Publication Type :
- Academic Journal
- Accession number :
- 177462210
- Full Text :
- https://doi.org/10.1007/s11127-022-01027-8