Linear-Time Algorithms for Proportional Apportionment
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.
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