Seat allocation distributions and seat biases of stationary apportionment methods for proportional representation

In a proportional representation system, apportionment methods are used to round the vote proportion of a party to an integer number of seats in parliament. Assuming uniformly distributed vote proportions, we derive the seat allocation distributions for stationary divisor methods. An important characteristic of apportionment methods are seat biases, that is, expected differences between actual seat numbers and ideal shares of seats, when the parties are ordered from largest to smallest. We obtain seat bias formulas for the stationary divisor methods and for the quota method of greatest remainders.Acknowledgement. We thank Friedrich Pukelsheim for many fruitful discussions.Received March 2004