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The probability of the Alabama paradox
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2012 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 49, no 3, 773-794 p.Article in journal (Refereed) Published
Abstract [en]

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 p(l), ..., p(m) 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.

Place, publisher, year, edition, pages
2012. Vol. 49, no 3, 773-794 p.
Keyword [en]
Alabama paradox, election method, apportionment, proportional allocation, Hamilton's method, method of largest remainder
National Category
URN: urn:nbn:se:uu:diva-183776DOI: 10.1239/jap/1346955333ISI: 000309151100014OAI: oai:DiVA.org:uu-183776DiVA: diva2:564579
Available from: 2012-11-02 Created: 2012-11-01 Last updated: 2013-03-04Bibliographically approved

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Janson, Svante
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