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The Probability of the Alabama Paradox

Part of: Mathematical economics Combinatorial probability

Published online by Cambridge University Press:  04 February 2016

Svante Janson  and
Svante Linusson
Svante Janson*
Affiliation:
Uppsala University
Svante Linusson*
Affiliation:
KTH - Royal Institute of Technology
*
∗ Postal address: Department of Mathematics, Uppsala University, PO Box 480, SE-751 06, Uppsala, Sweden. Email address: [email protected]
∗∗ Postal address: Department of Mathematics, KTH - Royal Institute of Technology, SE-100 44, Stockholm, Sweden. Email address: [email protected]
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Abstract

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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.

Keywords

Alabama paradoxelection methodapportionmentproportional allocationHamilton's methodmethod of largest remainder

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 91B12: Voting theory
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 773 - 794
Copyright
© Applied Probability Trust 

References

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