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A New Perspective on Impartial and Unbiased Apportionment

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  • Ross Hyman
  • Nicolaus Tideman

Abstract

How to fairly apportion congressional seats to states has been debated for centuries. We present an alternative perspective on apportionment, centered not on states but "families" of state, sets of states with "divisor-method" quotas with the same integer part. We develop ``impartial" and ``unbiased" apportionment methods. Impartial methods apportion the same number of seats to families of states containing the same total population, whether a family consists of many small-population states or a few large-population states. Unbiased methods apportion seats so that if states are drawn repeatedly from the same distribution, the expected number of seats apportioned to each family equals the expected divisor-method quota for that family.

Suggested Citation

  • Ross Hyman & Nicolaus Tideman, 2022. "A New Perspective on Impartial and Unbiased Apportionment," Papers 2201.11787, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2201.11787
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    File URL: http://arxiv.org/pdf/2201.11787
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