Seat biases of apportionment methods under general distributional assumptions

Abstract

Apportionment methods round vote proportions to integer numbers of seats in parliament. Seat biases of an apportionment method are expected differences between the seats actually apportioned to the parties and their ideal fractional shares of seats. In this letter it is shown that, for many popular apportionment methods, asymptotic seat biases for an increasing number of seats in parliament do not depend on the distributional assumption for the vote counts.