An Alternative Algorithm for U.S. House of Representatives Apportionment

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The apportionment of House seats to states after each decennial census can be viewed as a probability proportional to size (pps) sample allocation to the states. The sample size is 435, and the measure of size is the state's apportionment population (resident population plus U.S. federal employees and dependents living overseas, allocated to their home state), subject to the constraint that all states must receive at least one seat. An investigation of a group of sample allocations to areas that were supposed to be pps led to the discovery that the current method (Huntington-Hill) used for apportionment assigned excessive sample to areas with larger populations in the early sample assignment stages. An alternative algorithm was constructed that assigned sample to areas by minimizing the sum of the absolute values of the difference between the population proportion and the sample proportion across the areas at each stage. Subsequently the alternative algorithm was used to do a hypothetical apportionment following each census from 1790 and 2020. The results are similar or identical to Webster's method (used after the 1840, 1910, 1930 censuses).

Sample allocation 

Survey Research Methods Section