Linear-time algorithms for proportional apportionment

Abstract

The apportionment problem deals with the fair distribution of a discrete set of k indivisible resources (such as legislative seats) to n entities (such as parties or geographic subdivisions). Highest averages methods are a frequently used class of methods for solving this problem. We present an O(n)-time algorithm for performing apportionment under a large class of highest averages methods. Our algorithm works for all highest averages methods used in practice.