Public Choice

, Volume 99, Issue 3–4, pp 299–310 | Cite as

Robust voting

  • Gilbert W. BassettJr.
  • Joseph Persky


The formal equivalence between social choice and statistical estimation means that criteria used to evaluate estimators can be interpreted as features of voting rules. The robustness of an estimator means, in the context of social choice, insensitivity to departures from majority opinion. In this paper we consider the implications of substituting the median, a robust, high breakdown estimator, for Borda's mean. The robustness of the median makes the ranking method insensitive to outliers and reflect majority opinion. Among all methods that satisfy a majority condition, median ranks is the unique one that is monotonic. It is an attractive voting method when the goal is the collective assessment of the merits of alternatives.


Public Finance Statistical Estimation Social Choice Majority Opinion Ranking Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bassett, G.W. (1991). Equivariant, Monotone, 50% Breakdown Estimators. The American Statistician: 135–137.Google Scholar
  2. Bassett, G.W. and Persky, J. (1994). Rating skating. Journal of the American Statistical Association 89(427): 1075–1079.Google Scholar
  3. Hampel, F.R., Ronchetti, E., Rousseeuw, P.J. and Stahel, W.A. (1986). Robust statistics: The approach based on influence functions. New York: John Wiley & Sons.Google Scholar
  4. Hettmansperger, T.P. and Sheather, S.J. (1992). A cautionary note on the method of least median squares. The American Statistician 46: 79–83.Google Scholar
  5. Koenker, R. (1982). Robust methods in econometrics. Econometric Reviews 1: 213–225.Google Scholar
  6. Levin, J. and Nalebuff, B. (1995). An introduction to votecounting schemes. Journal of Economic Perspectives 9(1): 3–26.Google Scholar
  7. Levy, D. (1989). The statistical basis of AthenianAmerican constitutional theory. Journal of Legal Studies 18: 79–103.Google Scholar
  8. McLean I. (1995). Independence of irrelevant alternatives before Arrow. Mathematical Social Sciences 30: 107–126.Google Scholar
  9. McLean, I. and Urken, A.B. (1995). Classics of social choice theory. Ann Arbor: University of Michigan Press.Google Scholar
  10. Mosteller, F. and Tukey, J.W. (1977). Data analysis and regression. AddisonWesley.Google Scholar
  11. Nanson, E.J. ([1882], 1907). Methods of election, paper read to the Royal Society of Victoria on 12 October 1882, printed in Reports::: respecting the application of the principle of proportional representation to public elections, Cd. 3501. London: HMSO 1907. 123–141. In McLean and Urken (1995)Google Scholar
  12. Rousseeuw, P.J. (1984). Leastmedian of squares regression. Journal of the American Statistical Association 79(388), December.Google Scholar
  13. Rousseeuw, P.J. (1994). Unconventional features of positivebreakdown estimators. Statistics and Probability Letters 19(5): 417–431.Google Scholar
  14. Sen, A. (1995a). Rationality and social choice. American Economic Review 85(1): 1–24.Google Scholar
  15. Sen, A. (1995b). How to judge voting schemes. Journal of Economic Perspectives: 91–98.Google Scholar
  16. Small, C.G. (1990). A survey of multidimensional medians. International Statistical Review 58: 263–277.Google Scholar
  17. Young, H.P. (1988). Condorcet's theory of voting. American Political Science Review 82(4): 1231–1244.Google Scholar
  18. Young, H.P. (1995). Optimal voting rules. Journal of Economic Perspectives 9(1): 51–56.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Gilbert W. BassettJr.
    • 1
  • Joseph Persky
    • 1
  1. 1.Department of EconomicsUniversity of Illinois at ChicagoChicagoU.S.A

Personalised recommendations