Journal of Applied Probability

The probability of the Alabama paradox

Svante Janson and Svante Linusson

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Hamilton's method is a natural and common method to distribute seats proportionally between states (or parties) in a parliament. In the USA it has been abandoned due to some drawbacks, in particular the possibility of the Alabama paradox, but it is still in use in many other countries. In this paper we give, under certain assumptions, a closed formula for the asymptotic probability, as the number of seats tends to infinity, that the Alabama paradox occurs given the vector p1,..., pm of relative sizes of the states. From the formula we deduce a number of consequences. For example, the expected number of states that will suffer from the Alabama paradox is asymptotically bounded above by 1 / e and on average approximately 0.123.

Article information

Source
J. Appl. Probab., Volume 49, Number 3 (2012), 773-794.

Dates
First available in Project Euclid: 6 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1346955333

Digital Object Identifier
doi:10.1239/jap/1346955333

Mathematical Reviews number (MathSciNet)
MR3012099

Zentralblatt MATH identifier
1282.91092

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 91B12: Voting theory

Keywords
Alabama paradox election method apportionment proportional allocation Hamilton's method method of largest remainder

Citation

Janson, Svante; Linusson, Svante. The probability of the Alabama paradox. J. Appl. Probab. 49 (2012), no. 3, 773--794. doi:10.1239/jap/1346955333. https://projecteuclid.org/euclid.jap/1346955333


Export citation

References

  • Balinski, M. L. and Young, H. P. (2001). Fair Representation, 2nd edn. Brookings Institution Press, Washington, DC.
  • Billingsley, P. (1968). Convergence of Probability Measures. John Wiley, New York.
  • Fehndrich, M. (2005). Paradoxien von Hare/Niemeyer. Available at http://www.wahlrecht.de/verfahren/paradoxien/index.html.
  • Grafakos, L. (2004). Classical and Modern Fourier Analysis. Pearson, Upper Saddle River, NJ.
  • Janson, S. (2012). Asymptotic bias of some election methods. Ann. Operat. Res. 48pp. (elctronic).