Rule selection invariance as a robustness check in collective choice and nonparametric statistical settings

Shane Sanders (), Justin Ehrlich and James Boudreau
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Shane Sanders: Syracuse University
Justin Ehrlich: Syracuse University
James Boudreau: Department of Economics, Finance, and Quantitative Analysis, Kennesaw State University

Public Choice, 2024, vol. 199, issue 1, No 2, 7-26

Abstract: 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 $$\mathrm{n}

Keywords: Borda rule; Rank sum test; Sign test; Robustness check; Nonparametric statistics; Social choice; Public choice (search for similar items in EconPapers)
JEL-codes: C14 D71 D72 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11127-022-01027-8

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