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Proportional apportionment is the problem of assigning seats to partiesaccording to their relative share of votes. Divisor methods are the de-factostandard solution, used in many countries.  In recent literature, there are two algorithms that implement divisormethods: one by Cheng and Eppstein (ISAAC, 2014) has worst-case optimal runningtime but is complex, while the other (Pukelsheim, 2014) is relatively simpleand fast in practice but does not offer worst-case guarantees.  We demonstrate that the former algorithm is much slower than the other inpractice and propose a novel algorithm that avoids the shortcomings of both. Weinvestigate the running-time behavior of the three contenders in order todetermine which is most useful in practice.

A Practical and Worst-Case Efficient Algorithm for Divisor Methods of Apportionment