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The Probability Of The Alabama Paradox
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6339-2230
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:kth:diva-104145DOI: 10.1239/jap/1346955333ISI: 000309151100014ScopusID: 2-s2.0-84872176767OAI: diva2:563673
Knut and Alice Wallenberg Foundation

QC 20121031

Available from: 2012-10-31 Created: 2012-10-29 Last updated: 2012-10-31Bibliographically approved

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Linusson, Svante
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