Seat excess variances of apportionment methods for proportional representation

Apportionment methods round vote proportions to integer numbers of seats in a parliament. The seat excess is the difference between the integer seat allocation and the fractional ideal share of seats. In order to quantify biased treatment of larger versus smaller parties, previous studies derived the conditional expectation of the seat excess, when the vote proportions are conditioned to be ordered. We complement these studies by computing the conditional seat excess variance for popular apportionment methods.