# Asymptotic bias of some election methods

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## Abstract

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.

## Keywords

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

### Acknowledgement

I thank Friedrich Pukelsheim for many helpful comments.

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