Asymptotic bias of some election methods

Consider an election where N seats are distributed among parties with proportions p1,…,pm 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 Npi that yields exact proportionality. Our approach is to keep p1,…,pm 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.

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