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 tend to infinity, 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.Comment: 54 page