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

Author

Listed:
  • Shane Sanders

    (Syracuse University)

  • Justin Ehrlich

    (Syracuse University)

  • James Boudreau

    (Department of Economics, Finance, and Quantitative Analysis, Kennesaw State University)

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}

Suggested Citation

  • Shane Sanders & Justin Ehrlich & James Boudreau, 2024. "Rule selection invariance as a robustness check in collective choice and nonparametric statistical settings," Public Choice, Springer, vol. 199(1), pages 7-26, April.
    • Handle: RePEc:kap:pubcho:v:199:y:2024:i:1:d:10.1007_s11127-022-01027-8
    DOI: 10.1007/s11127-022-01027-8
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    References listed on IDEAS

    as
    1. Onur Doğan & Ayça Giritligil, 2014. "Implementing the Borda outcome via truncated scoring rules: a computational study," Public Choice, Springer, vol. 159(1), pages 83-98, April.
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    5. Simon Medcalfe, 2018. "Economic Well-Being in U.S. Metropolitan Statistical Areas," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(3), pages 1147-1167, October.
    6. 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.
    7. Boudreau, James & Ehrlich, Justin & Sanders, Shane & Winn, Adam, 2014. "Social choice violations in rank sum scoring: A formalization of conditions and corrective probability computations," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 20-29.
    8. 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.
    9. Franklin G. Mixon Jr. & Ernest W. King, 2012. "Social Choice Theory in 10,000 Meters: Examining Independence and Transitivity in the Ncaa Cross-Country Championships," The American Economist, Sage Publications, vol. 57(1), pages 32-41, May.
    10. Justin Ehrlich & Simon Medcalfe & Shane Sanders, 2021. "Composite Index Ranking of Economic Well-Being in U.S. Metropolitan Areas: How Prevalent are Rank Anomalies?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 157(2), pages 543-562, September.
    11. Eerik Lagerspetz, 2016. "Plurality, approval, or Borda? A nineteenth century dispute on voting rules," Public Choice, Springer, vol. 168(3), pages 265-277, September.
    12. Drora Karotkin & Shmuel Nitzan, 1996. "A note on restricted majority rules: invariance to rule selection and outcome distinctiveness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(3), pages 269-274.
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    More about this item

    Keywords

    Borda rule; Rank sum test; Sign test; Robustness check; Nonparametric statistics; Social choice; Public choice;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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