Annals of Operations Research

, Volume 215, Issue 1, pp 89–136 | Cite as

Asymptotic bias of some election methods

  • Svante JansonEmail author


Consider an election where N seats are distributed among parties with proportions p 1,…,p m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a party, i.e. the difference between the number of seats given to the party and the (real) number Np i that yields exact proportionality. Our approach is to keep p 1,…,p m fixed and let N→∞, with N random in a suitable way.

In particular, we give formulas showing the bias favouring large or small parties for the different election methods.


Proportional election methods Divisor methods Quota methods Bias Probability of violating quota Apparentements 



I thank Friedrich Pukelsheim for many helpful comments.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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